Single antenna interference suppression in a wireless receiver

ABSTRACT

A novel and useful apparatus for and method of single antenna interference cancellation (SAIC) in a wireless communications system. A class of algorithms for Downlink Advanced Receiver Performance (DARP) receivers based on a novel metric calculation used during equalization and optionally in other portions of the receiver as well such as soft value generation. A DARP receiver for 8PSK EDGE modulation is presented wherein the interfering signals comprise GMSK modulated signals In accordance with the invention, the modified metric is adapted to take into account the rotation remaining in the noise component of the received signal after de-rotation of the 8PSK signal. Considering the interferer to be a GMSK signal, the I/Q elements of the noise are correlated and this fact is used to modify the decision rule for the received signal thus improving the performance of the equalizer. The model is further extended to take into account temporal error correlation.

REFERENCE TO PRIORITY APPLICATION

This application claims priority to U.S. Provisional Application Ser.No. 60/660,206, filed Mar. 10, 2005, entitled “Single AntennaInterference Cancellation,” incorporated herein by reference in itsentirety.

FIELD OF THE INVENTION

The present invention relates generally to wireless communicationsystems and more particularly relates to an apparatus and method ofsingle antenna interference cancellation for use in 8PSK EDGE receivers.

BACKGROUND OF THE INVENTION

In recent years, the world has witnessed explosive growth in the demandfor wireless communications and it is predicted that this demand willincrease in the future. There are already over 1.5 billion userssubscribing to cellular telephone services and the number is continuallyincreasing. The number of GSM users around the world alone has alreadycrossed the 1.2 billion mark, as an example of the increased use ofcellular services. One in five people around the world now has a mobilephone and in some developed markets mobile penetration has alreadyapproached 100%. It is predicted that by 2010 there will be over 2.3billion individual wireless subscribers worldwide.

In some countries, the number of cellular subscribers already exceedsthe number of fixed line telephone installations. In many cases, therevenues from mobile services exceeds that for fixed line services eventhough the amount of traffic generated through mobile phones is lessthan in fixed networks.

Other related wireless technologies have experienced growth similar tothat of cellular. For example, cordless telephony, two way radiotrunking systems, paging (one way and two way), messaging, wirelesslocal area networks (WLANs), wireless local loops (WLLs), WiMAX andUltra Wideband (UWB) based MANs.

Currently, the majority of users subscribe to digital cellular networks.Almost all new cellular handsets sold to customers are based on digitaltechnology, typically third generation digital technology. Currently,fourth generation digital networks are being designed and tested whichwill be able to support data packet networks and much higher data rates.The first generation analog systems comprise the well known protocolsAMPS, TACS, etc. The digital systems comprise GSM/GPRS/EGPRS, TDMA(IS-136), CDMA (IS-95), UMTS (WCDMA), etc. Future fourth generationcellular services are intended to provide mobile data at rates of 100Mbps or more.

A problem exists in wireless communication systems such as GSM, however,where stray signals, or signals intentionally introduced by frequencyreuse methods, can interfere with the proper transmission and receptionof voice and data signals and can lower capacity. The constant increasein the deployment of cellular networks increases both the levels ofbackground interference and interference due to co-channel transmission.For typical cell layouts, the major source of noise and interferenceexperienced by GSM communication devices when the network is supportinga non-trivial number of users is due to co-channel and/or adjacentchannel interference. Such noise sources arise from nearby devicestransmitting on or near the same channel as the desired signal, or fromadjacent channel interference, such as noise arising on the desiredchannel due to spectral leakage. A diagram illustrating an examplecellular network including a plurality of EDGE transmitters andreceivers and GMSK transmitters generating co-channel interference isshown in FIG. 1. The example cellular network, generally referenced 100,comprise an EDGE transmitter 102 and receiver 106 for sending andreceiving a main, desired signal. A plurality of GSM transmitters 104,outputting a GMSK signal, generate co-channel interference at the EDGEreceiver 106.

This interference from these noise sources is sensed in both mobileterminals and base stations. In areas with dense cellular utilization asevere degradation in network performance is reported due to thiseffect. Furthermore, cellular operators with low network bandwidth areforced to lower the reuse factor in their networks which furtherincreases the rate of channel co-transmissions. The problem ofco-channel transmissions poses a disjoint problem for both the receiverat the base station and the receiver at the mobile station.

For the base station the co-channel interference problem is consideredsimpler than in the case of mobile terminals. One reason for that isthat the higher cost of base station equipment permits the insertion ofcomplex receivers to combat the sensed interferences. The receivers inthe base station (1) incorporate algorithms with higher levels ofcomplexity, (2) can have higher power consumption, etc. Another reasonthe co-channel interference problem is considered simpler in the basestation than in the case of mobile terminals is that the base stationcan utilize smart antennas to help deal with the problem of co-channelinterference. Although smart antennas will affect the cost of the basestation, its main impact is in the physical size of the antenna. Due tothe size of the smart antenna, its use with mobile, portable cellularequipment is severely limited. It use with base stations, however, isnot limited considering the static relatively large sized antennaspermitted for base stations. The size of base station antennas ispractically unbounded and therefore the usage of smart phased arrayantennas is possible. This enables the use of receive diversitytechniques with multi user separation capability.

In the mobile terminal, on the other hand, both complexity and size arecrucial factors in the applicability of a solution. Firstly, complexsolutions lead to high MIPS consumption which typically causes increasedpower consumption as well as increased costs. Secondly, the physicalsize of the mobile terminal is limited. The tiny size of pocket-sizedmobile terminals today substantially limits the expected effectivenessin choosing a smart antenna solution, leaving them for base stationapplications only.

Therefore, in order for cellular networks to remain effective, there isrenewed interest in simple interference reduction solutions that areapplicable with a single antenna input. Recently, there is greatinterest in developing an effective interference reduction solution withregards to GSM networks especially for voice applications. This isbecause the coverage of EGPRS services is expected to increase greatlyand it is expected that existing GSM transmissions will be appear asco-channel interference to EDGE receivers.

Prior art solutions to the problem can generally be divided into twofamilies: (1) joint solutions where some kind of knowledge about theinterference is assumed such as a known training sequence (TSC) and (2)blind solutions where no a priori knowledge regarding the interferingsignal is undertaken. The first family, which is considered to result ina more complex solution, may be separated into two subsets: (a)iterative solutions and (b) joint solutions. Iterative solutionscorrespond to a receiver where the strongest signal is first demodulatedand then in a second step, a residual error signal from the first stepis demodulated to estimate the co-existing signal (which may be the mainsignal of interest and the interfering signal as well). This iterationmay be performed many times until a stopping criterion is fulfilled. Injoint solutions the main signal and the interfering signal are jointlydemodulated assuming a joint received signal model.

A blind solution, on the other hand, does not assume any a prioriknowledge about the interfering signal. The most common approach takenis to use a higher order statistics model for the interfering signal.Although, a blind solution is expected to be advantageous in terms ofcomplexity and robustness, it is usually at the expense of performance.

Many prior art interference cancellation techniques have focused onadjacent channel suppression which uses several filtering operations tosuppress the frequencies of the received signal that are not alsooccupied by the desired signal. Co-channel interference techniques, suchas joint demodulation, generally require joint channel estimationmethods to provide a joint determination of the desired and co-channelinterfering signal channel impulse responses. Given known trainingsequences, all the co-channel interferers can be estimated jointly. Thisjoint demodulation technique, however, consumes a large number of MIPSprocessing, which limits the number of equalization parameters that canbe used efficiently. Moreover, classical joint demodulation onlyaddresses one co-channel interferer, and does not address adjacentchannel interference.

Multiple antenna techniques have also been proposed but these arecomplex in terms of hardware implementation and therefore are suited tobase station applications but not mobile applications. Further, all ofthe above techniques are non-trivial in implementation and/orcomplexity.

Thus, there is a need for a Single Antenna Interference Cancellation(SAIC) solution for reducing the effect of co-channel interferingsignals that is suitable for implementation in mobile handsets, isrelatively simple to implement, does not have high MIPS consumption anddoes not significantly increase cost.

SUMMARY OF THE INVENTION

Accordingly, the present invention provides a novel and useful apparatusfor and method of single antenna interference cancellation (SAIC) in awireless communications system. The present invention is suitable foruse with a wide range of channels and is particularly useful in reducingthe effects of co-channel interference caused by in-band transmissionsof other modulation schemes that are received by the mobile handset. Atypical application of the SAIC based algorithms provided by the presentinvention is with reducing co-channel interference such as GMSKmodulation in EDGE enabled networks.

To aid in illustrating the principles of the present invention, theapparatus and method are presented in the context of a GSM EDGE mobilestation. It is not intended that the scope of the invention be limitedto the examples presented herein. One skilled in the art can apply theprinciples of the present invention to numerous other types ofcommunication systems as well without departing from the scope of theinvention.

The present invention provides a novel class of algorithms for DownlinkAdvanced Receiver Performance (DARP) receivers. The proposed approach isbased on a novel metric calculation used during equalization andoptionally in other portions of the receiver as well such as the softvalue generator. Existing equalizers can be modified to implement theSAIC algorithms of the present invention. In terms of complexity,however, the receiver remains similar to the conventional equalizeremployed. In terms of memory, that no additional memory is required toconstruct the trellis based equalizer. In terms of computing resources,however, there is an increase in required resources due to an increasein the complexity of the branch metric model. The required increase inreceiver complexity, however, is minimal when compared to the computingrequirements of prior art solutions.

In accordance with the invention, the modified metric is adapted to takeinto account the rotation remaining in the noise component of thereceived signal after 8PSK de-rotation is applied. Considering theinterferer to be a GMSK signal, a key assumption made is that the I/Qelements of the noise are correlated. This known correlation is thenused to modify the decision rule for the received signal thus improvingthe performance of the equalizer. The model is further extended to takeinto account temporal error correlation.

The scope of this document is to present a DARP receiver for 8PSK EDGEmodulation wherein the interfering signals comprise GMSK modulatedsignals. Note that throughout this document the term GMSK denotes bothGSM and GPRS modulation schemes. The solution presented by the presentinvention is blind and is therefore sufficiently robust for use in manywell-known testing scenarios. It is noted that the blind receiverapproach taken by the present invention is capable of improving theperformance of a reference receiver by 2.5 dB for a static channel andby approximately 1 dB for the TU3 iFH channel. In addition, similarimprovements are observed for the case of unsynchronized network testingscenarios. Furthermore, the proposed algorithm does not reduceperformance in conventional testing scenarios.

There is therefore provided in accordance with the invention, a methodof computing a metric to be used in determining an estimate of a mostlikely sequence of symbols transmitted over a channel from a pluralityof received samples, each received sample comprising an informationcomponent and an interference component, the method comprising the stepsof estimating an error vector by subtracting the convolution of knowntraining sequence symbols with an estimate of the channel from theplurality of received samples corresponding to the training sequence,estimating a noise correlation matrix by processing real and imaginarycomponents of the error vector, computing a plurality of summations byprocessing the plurality of received samples, the noise correlationmatrix and a plurality of hypotheses of symbols that have been passedthrough the channel and determining a minimum summation from theplurality of summations resulting in the metric.

There is also provided in accordance with the invention, a method ofcomputing a metric to be used in determining, from a plurality ofreceived samples, an estimate of a most likely sequence of symbolstransmitted over a channel, each received sample comprising aninformation component and an interference component, the methodcomprising the steps of estimating an error vector by subtracting theconvolution of known training sequence symbols with an estimate of thechannel from the plurality of received samples corresponding to thetraining sequence, de-rotating the error vector to generate a de-rotatederror vector, estimating a noise correlation matrix by processing realand imaginary components of the de-rotated error vector, computing arotation compensated noise correlation matrix by processing the noisecorrelation matrix in accordance with a corresponding sample index,computing a plurality of summations by processing the plurality ofreceived samples, the rotation compensated noise correlation matrix anda plurality of hypotheses of symbols that have been passed through thechannel and determining a minimum summation from the plurality ofsummations resulting in the metric.

There is further provided in accordance with the invention, a method ofimplementing an equalizer in a radio receiver subjected to co-channelinterference, the method comprising the steps of receiving a pluralityof received samples, each received sample comprising an informationcomponent and an interference component, calculating and assigning ametric to each sequence of symbols to be considered, wherein the step ofcalculating the metric comprises the steps of estimating an error vectorby subtracting the convolution of known training sequence symbols withan estimate of the channel from the plurality of received samplescorresponding to the training sequence, de-rotating the error vector togenerate a de-rotated error vector, estimating a noise correlationmatrix by processing real and imaginary components of the de-rotatederror vector, computing a rotation compensated noise correlation matrixby processing the noise correlation matrix in accordance with acorresponding sample index, computing a plurality of summations byprocessing the plurality of received samples, the rotation compensatednoise correlation matrix and a plurality of hypotheses of symbols thathave been passed through the channel, determining a minimum summationfrom the plurality of summations resulting in a lowest metricrepresenting a most likely sequence of symbols transmitted over thechannel and removing intersymbol interference introduced by the channelincluding the co-channel interference utilizing the lowest metric.

There is also provided in accordance with the invention, a computerprogram product characterized by that upon loading it into computermemory a metric calculation process is executed, the computer programproduct comprising a computer useable medium having computer readableprogram code means embodied in the medium for computing a metric to beused in determining an estimate of a most likely sequence of symbolstransmitted over a channel from a plurality of received samples, eachreceived sample comprising an information component and an interferencecomponent, the computer program product comprising computer readableprogram code means for estimating an error vector by subtracting theconvolution of known training sequence symbols with an estimate of thechannel from the plurality of received samples corresponding to thetraining sequence, computer readable program code means for estimating anoise correlation matrix by processing real and imaginary components ofthe rotated error vector, computer readable program code means forcomputing a plurality of summations by processing the plurality ofreceived samples, the noise correlation matrix and a plurality ofhypotheses of symbols that have been passed through the channel andcomputer readable program code means for determining a minimum summationfrom the plurality of summations resulting in the metric.

There is further provided in accordance with the invention, a radioreceiver coupled to a single antenna comprising a radio frequency (RF)receiver front end circuit for receiving a radio signal transmitted overa channel and downconverting the received radio signal to a basebandsignal, the received radio signal comprising an information componentand an interference component, a demodulator adapted to demodulate thebaseband signal in accordance with the modulation scheme used togenerate the transmitted radio signal, a channel estimation moduleadapted to calculate a channel estimate by processing a receivedtraining sequence and a known training sequence, an equalizer adapted toremove intersymbol interference introduced by the channel utilizing ametric calculation stage and an estimate of the channel, the metriccalculation stage comprising processing means adapted to, estimate anerror vector by subtracting the convolution of known training sequencesymbols with the estimate of the channel from the plurality of receivedsamples corresponding to the training sequence, estimate a noisecorrelation matrix by processing real and imaginary components of the=error vector, compute a plurality of summations by processing theplurality of received samples, the noise correlation matrix and aplurality of hypotheses of symbols that have been passed through thechannel, determine a minimum summation from the plurality of summationsresulting in the metric and a decoder adapted to decode the output ofthe equalizer to generate output data therefrom.

There is also provided in accordance with the invention, a method ofgenerating soft values from hard symbol decisions output of anequalizer, the method comprising the steps of calculating an errormatrix incorporating consideration for I/Q correlation of noise in aninterferer signal, estimating an error vector by subtracting theconvolution of known training sequence symbols with an estimate of thechannel from a plurality of received samples corresponding to thetraining sequence, estimating a noise correlation matrix by processingreal and imaginary components of the error vector, computing a pluralityof summations by processing the plurality of received samples, the noisecorrelation matrix and a plurality of hypotheses of symbols that havebeen passed through the channel, determining a minimum summation fromthe plurality of summations resulting in an error metric, determining aconditional probability of the plurality of received samples given thehard symbol decision sequence and calculating log likelihood ratio (LLR)of the conditional probability to yield the soft decision values.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is herein described, by way of example only, withreference to the accompanying drawings, wherein:

FIG. 1 is a diagram illustrating an example cellular network including aplurality of EDGE transmitters and receivers and GMSK transmittersgenerating co-channel interference;

FIG. 2 is a block diagram illustrating an example EDGE transceiverconstructed in accordance with the present invention;

FIG. 3 is a diagram illustrating the decision regions for MinimumEuclidian Distance (MED) criterion;

FIG. 4 is a diagram illustrating the decision regions for MinimumEuclidian Distance (MED) criterion with I/Q correlated noise;

FIG. 5 is a diagram illustrating modeling an 8PSK signal with a BPSKinterfering signal;

FIG. 6 is a diagram illustrating modeling of a GMSK interferer asrotated I/Q correlated noise;

FIG. 7 is a block diagram illustrating an error vector calculationapparatus as contemplated by the present invention used in cancelingco-channel interference;

FIGS. 8A through 8H are diagrams illustrating the decision regions forrotated correlation matrices;

FIG. 9 is a graph illustrating symbol error rate (SER) versus SNR whenusing the correct correlation matrix for correlated noise;

FIG. 10 is a trellis diagram illustrating the effect of a competitorsymbol on the cumulative metric calculation;

FIG. 11 is a graph illustrating simulation results for a receiverimplementing the SAIC scheme of the present invention;

FIG. 12 is a block diagram illustrating the processing blocks of a GSMEGPRS mobile station in more detail including RF, baseband and signalprocessing blocks; and

FIG. 13 is a block diagram illustrating an example computer processingsystem adapted to perform the SAIC scheme of the present invention.

DETAILED DESCRIPTION OF THE INVENTION Notation Used Throughout

The following notation is used throughout this document. Term Definition8PSK 8 Phase Shift Keying AMPS Advanced Mobile Telephone System ARAutoregressive ASIC Application Specific Integrated Circuit AWGNAdditive White Gaussian Noise BLER Block Error Rate BPSK Binary PhaseShift Keying CDMA Code Division Multiple Access CD-ROM Compact Disc ReadOnly Memory CPU Central Processing Unit CRC Cyclic Redundancy Check DFEDecision Feedback Equalizer DSL Digital Subscriber Line DSP DigitalSignal Processor EDGE Enhanced Data for Global Evolution EEROMElectrically Erasable Read Only Memory EGPRS Enhanced General PacketRadio System FEC Forward Error Correction FIR Finite Impulse ResponseFPGA Field Programmable Gate Array FTP File Transfer Protocol GERAN GSMEDGE Radio Access Network GMSK Gaussian Minimum Shift Keying GPRSGeneral Packet Radio System GSM Global System for Mobile CommunicationHTTP Hyper Text Transport Protocol IID Independent and IdenticallyDistributed ISDN Integrated Services Digital Network ISI IntersymbolInterference LLR Log Likelihood Ratio MAN Metropolitan Area Network MEDMinimum Euclidian Distance MIPS Millions of Instructions Per Second MLSEMaximum Likelihood Sequence Estimation MMSE Minimum Mean Square ErrorMSE Mean Squared Error PDF Probability Density Function PSK Phase ShiftKeying PSP Per Survivor Processing QAM Quadrature Amplitude ModulationRF Radio Frequency ROM Read Only Memory SAIC Single Antenna InterferenceCancellation SER Symbol Error Rate SNR Signal to Noise Ration SVG SoftValue Generator TACS Total Access Communications Systems TDMA TimeDivision Multiple Access TSC Training Sequence UMTS Universal MobileTelecommunications System UWB Ultrawideband VA Viterbi Algorithm WCDMAWideband Code Division Multiple Access WiMAX Worldwide Interoperabilityfor Microwave Access WLAN Wireless Local Area Network WLL Wireless LocalLoop WMF Whitening Matched Filter

Detailed Description of the Invention

The present invention is an apparatus for and method of single antennainterference cancellation (SAIC) for used in a wireless communicationssystem. Examples of wireless communications systems include cordlesstelephony and cellular communications systems. Examples of cellularcommunications systems include global systems for mobile communications(GSM), CDMA, TDMA, etc. The present invention is suitable for use with awide range of channels and is particular useful in reducing the effectsof co-channel interference caused by in-band transmissions of othermodulation schemes that are received by the mobile handset. A typicalapplication of the SAIC based algorithms provided by the presentinvention is with reducing co-channel interference such as GMSKmodulation in EDGE enabled networks.

To aid in illustrating the principles of the present invention, theapparatus and method are presented in the context of a GSM EDGE mobilestation. It is not intended that the scope of the invention be limitedto the examples presented herein. One skilled in the art can apply theprinciples of the present invention to numerous other types ofcommunication systems as well without departing from the scope of theinvention.

Note that the receiver configuration presented herein is intended forillustration purposes only and is not meant to limit the scope of thepresent invention. It is appreciated that one skilled in thecommunication and signal processing arts can apply the SAIC algorithmsand modified metrics of the present invention to numerous other receivertopologies and communication schemes as well.

Received Signal Model

The invention assumes the following model for received signals. Consideran 8PSK modulated (i.e. $\frac{3\pi}{8}$rotated) received signal with a coexisting combination of GMSKinterfering signal as follows: $\begin{matrix}{y_{i} = {{\sum\limits_{k = 0}^{L - 1}{h_{k}x_{i - k}}} + {\sum\limits_{k = 0}^{L_{g} - 1}{g_{k}x_{i - k}^{co}}} + {\sqrt{\frac{N_{0}}{2}}n_{i}}}} & (1)\end{matrix}$where

-   -   y_(i) represents the received signal samples;    -   L denotes the channel order (or length in sampling time units);    -   h_(k) represents the channel taps of the signal of interest;    -   g_(k) represents the channel taps of the interfering signal;    -   x_(i) denotes the transmitted symbols (8PSK after de-rotation);    -   x^(co) denotes the co-channel, offset rotated, symbols;        Accordingly, L_(g), denotes the co-channel interference        channel-order with channel taps g_(k). The noise sequence,        denoted n_(i), is a zero-mean unit-variance independent and        identically distributed (IID) sequence. Note that the noise        probability density function (PDF) is circularly-symmetric        complex-normal random variables (i.e., n_(i)≈CN(0,I_(2×2))). N        denotes the additive white Gaussian noise (i.e., n_(i) AWGN)        single sided power spectral density. In this model we assume        that x^(co) is a $\frac{\pi}{8}$        rotated GMSK modulated signal. The $\frac{3\pi}{8}$        de-rotation of the 8PSK signal results in a marginal rotation of        $\frac{\pi}{8}$        for the co-channel interference. The assumption of the        interfering signal may be easily extended for 8PSK signals as        well. As is described infra in the interference reduction        algorithm description many aspects of the blind solution        formulation may also be advanced for the GMSK/GMSK scenario.

Example EDGE Receiver

A block diagram illustrating an example EDGE transceiver constructed inaccordance with the present invention is shown in FIG. 2. Thecommunications transceiver, generally referenced 200, is coupled to anantenna 202 and comprises a transmitter 220 and receiver 240. Thereceiver 240 comprises an RF front-end 204, demodulator (de-rotator)206, channel estimation 218, equalizer (i.e. inner decoder) 208, softvalue generator 212, metric calculation 210, de-interleaver 214 andouter decoder 216. The signal supplied by the antenna is sent throughfrom channel from the transmitter 102 FIG. 1). The concatenated encodertransmitter 220, for example, comprises an encoder 222, interleaver 224,bit to symbol mapper 226, modulator 228 and transmit circuit 230.

In the transmitter, input data bits to be transmitted are input to theencoder 222 which may comprise an error correction encoder such as ReedSolomon, convolutional encoder, parity bit generator, etc. The encoderfunctions to add redundancy bits to enable errors in transmission to belocated and fixed.

The bits output of the encoder are then input to the interleaver 224which functions to rearrange the order of the bits in order to moreeffectively combat error bursts in the channel. The bits output of theinterleaver are then mapped to symbols by the symbol mapper 226. The bitto symbol mapper functions to transform bits to modulator symbols froman M-ary alphabet. For example, an 8PSK modulator converts input bitsinto one of eight symbols. Thus, the mapper in this case generates asymbol for every three input bits.

The symbols output from the mapper are input to the modulator 228 whichfunctions to receive symbols in the M-ary alphabet and to generate ananalog signal therefrom. The transmit circuit 230 filters and amplifiesthis signal before transmitting it over the channel. The transmitcircuit comprises coupling circuitry required to optimally interface thesignal to the channel medium.

The channel may comprise a mobile wireless channel, e.g., cellular,cordless, fixed wireless channel, e.g., satellite, or may comprise awired channel, e.g., xDSL, ISDN, Ethernet, etc. It is assumed that AWGNand co-channel interference generated by adjacent GMSK transmitters arepresent which is added to the signal in the channel. The transmitter isadapted to generate a signal that can be transmitted over the channel soas to provide robust, error free detection by the receiver.

It is noted that both the inner and outer decoders in the receiver havecomplimentary encoders in the system. The outer encoder in the systemcomprises the encoder, e.g., convolutional, etc. The inner encodercomprises the channel itself, which in one embodiment can be modeled asan L-symbol long FIR-type channel.

At the receiver, the analog signal from the channel is input to RF frontend circuitry 204 via antenna 202. The front-end circuitry anddemodulator function to downconvert and sample the received signal togenerate received samples at the symbol rate. Assuming a receiveradapted to receive an EDGE modulated signal, the samples comprising acomplete burst are collected and subsequently split into trainingsequence samples and data samples. The data samples are input to theequalizer 208 while the training sequence samples are input to a channelestimation module 218 which functions to calculate a channel estimatethat is input to the equalizer. The channel estimate is generated usingthe received training sequence samples and the known or referencetraining sequence.

Several methods of channel estimation and channel order selection areknown in the art and suitable for use with the present inventioninclude, for example U.S. Pat. No. 6,907,092, entitled Method Of ChannelOrder Selection And Channel Estimation In A Wireless Communication“System,” incorporated herein by reference in its entirety.

The inner decoder (i.e. the equalizer) is operative to generatedecisions from the data samples. An example of an inner decoder is anequalizer which compensates for the ISI caused by the delay and timespreading of the channel. The function of the equalizer is to attempt todetect the symbols that were originally transmitted by the modulator.The equalizer is adapted to output symbol decisions and may comprise,for example the well known maximum likelihood sequence estimation (MLSE)based equalizer that utilizes the well known Viterbi Algorithm (VA),linear equalizer or decision feedback equalizer (DFE).

Most communication systems must combat a problem known as IntersymbolInterference (ISI). Ideally, a transmitted symbol should arrive at thereceiver undistorted, possibly attenuated greatly and occupying only itstime interval. In reality, however, this is rarely the case and thereceived symbols are subject to ISI. Intersymbol interference occurswhen one symbol is distorted sufficiently that is occupies timeintervals of other symbols.

The situation is made even worse in GSM communications systems as theGSM transmitter contributes its own ISI due to controlled and deliberateISI from the transmitter's partial response modulator. The effects ofISI are influenced by the modulation scheme and the signaling techniquesused in the radio.

Equalization is a well known technique used to combat intersymbolinterference whereby the receiver attempts to compensate for the effectsof the channel on the transmitted symbols. An equalizer attempts todetermine the transmitted data from the received distorted symbols usingan estimate of the channel that caused the distortions. Incommunications systems where ISI arises due to partial responsemodulation or a frequency selective channel, a maximum likelihoodsequence estimation (MLSE) equalizer is optimal. This is the form ofequalizer generally used in GSM, EDGE and GERAN systems.

The MLSE technique is a nonlinear equalization technique which isapplicable when the radio channel can be modeled as a Finite ImpulseResponse (FIR) system. Such a FIR system requires knowledge of thechannel impulse response tap values. As described supra, the channelestimate is obtained using a known training symbol sequence to estimatethe channel impulse response. Other equalization techniques such as DFEor linear equalization require precise knowledge of channel.

There exist other equalization techniques such as Decision FeedbackEqualization (DFE) or linear equalization. All these equalizationtechniques require precise knowledge of channel.

In GSM, the training sequence is sent in the middle of each burst. AsEach fixed length burst consists of 142 symbols preceded by 3 tailsymbols and followed by 3 tail symbols and 8.25 guard symbols. The 142symbols include a 58 symbol data portion, 26 symbol training sequenceand another 58 symbol data portion. Since the training sequence is sentin the middle of the burst, it is referred to as a midamble. It isinserted in the middle of the burst in order to minimize the maximumdistance to a data bit thus minimizing the time varying effects at theends of the burst.

The training sequences comprise sequences of symbols generated to yieldgood autocorrelation properties. The receiver control algorithm uses thetraining sequence, received in the presence of ISI, to determine thecharacteristics of the channel that would have generated the symbolsactually received. GSM uses eight different training sequences wherebythe autocorrelation of each results in a central peak surrounded byzeros. The channel impulse response can be measured by correlating thestored training sequence with the received sequence.

The MLSE equalizer (also called a Viterbi equalizer) uses the Viterbialgorithm along with inputs and an estimate of the channel to extractthe data. The equalizer generates a model of the radio transmissionchannel and uses this model in determining the most likely sequence. Anestimate of the transfer function of the channel is required by the MLSEequalizer in order to be able to compensate for the channel ISI effect.

The MLSE equalizer operates by scanning all possible data sequences thatcould have been transmitted, computing the corresponding receiver inputsequences, comparing them with the actual input sequences received bycomputing the modified metric of the present invention in accordancewith the parameters and selects the sequence yielding the highestlikelihood of being transmitted. Considering that ISI can be viewed asunintentional coding by the channel, the Viterbi algorithm used in theMLSE equalizer can be effective not only in decoding convolutional codesequences but in combating ISI. Typically, the MLSE equalizer comprisesa matched filter (i.e. FIR filter) having L taps coupled to a Viterbiprocessor. The output of the equalizer is input to the Viterbi processorwhich finds the most likely data sequence transmitted.

The channel estimate is used by the equalizer in processing the datablocks on either side of the training sequence midamble. A trackingmodule may be used to improve the performance of the receiver. If atracking module is employed, the equalizer is operative to use theinitial channel estimate in generating hard decisions for the firstblock of data samples. Decisions for subsequent data blocks aregenerated using updated channel estimates provided by the trackingmodule. The equalizer is also operative to generate preliminarydecisions which are used by the tracking module in computing therecursive equations for the updated channel estimate.

The output of the equalizer comprises hard symbol decisions. The harddecisions are then input to the soft value generator 212 which isoperative to output soft decision information given (1) hard symboldecisions from the inner decoder, (2) channel model information h(k),and (3) the input samples received from the channel.

The soft decision information for a symbol is derived by determining theconditional probability of the input sample sequence given the hardsymbol decision sequence. The soft decision is calculated in the form ofthe log likelihood ratio (LLR) of the conditional probability. The noisevariance of the channel also used by the soft value generator ingenerating the soft information. A soft symbol generator suitable foruse with the present invention is described in more detail in U.S. Pat.No. 6,731,700, entitled “Soft Decision Output Generator,” incorporatedherein by reference in its entirety.

The log likelihood ratio is defined as the ratio of the probability of afirst symbol with a second symbol wherein the second symbol is areference symbol. The reference symbol is arbitrary as long as it isused consistently for all the soft output values for a particular timek. The reference symbol can, however, vary from time k+1, k+2, etc.Preferably, however, the reference is kept the same throughout.

Note that a hard decision is one of the possible values a symbol cantake. In the ideal case, a soft decision comprises the reliabilities ofeach possible symbol value. The soft decision comprises a completeinformation packet that is needed by the decoder. An information packetis defined as the output generated by a detector or decoder in a singleoperation.

The soft decision information output of the soft value generator isinput to the outer decoder 216 which is preferably an optimal softdecoder. The outer decoder functions to detect and fix errors using theredundancy bits inserted by the encoder and to generate the binaryreceive data. Examples of the outer decoder include convolutionaldecoders utilizing the Viterbi Algorithm, convolutional Forward ErrorCorrection (FEC) decoders, turbo decoders, etc. Soft input Viterbidecoders have the advantage of efficiently processing soft decisioninformation and providing optimum performance in the sense of minimumsequence error probability.

Note that optionally, a de-interleaver 214 may be used in the receiver(and correspondingly in the transmitter). In this case, a symbol basedinterleaver/de-interleaver is used to reconstruct the original order ofthe data input to the transmitter. If a bit basedinterleaver/de-interleaver is used, a mechanism of mapping soft symbolsto bits must be used before the outer decoder, such as described in U.S.Pat. No. 6,944,242, entitled “Apparatus For And Method Of ConvertingSoft Symbol Information To Soft Bit Information,” incorporated herein byreference in its entirety.

Error Metric Modification (De-Correlation)

As described supra, the objective of the equalizer is to find the mostlikely sequence of transmitted symbols, given a buffer of receivedsymbols. This well-known process is referred to as Maximum LikelihoodSequence Estimation (MLSE). In order to select the best sequence, theequalizer essentially assigns a metric to each sequence. After computingthe metric for all sequences, it selects the sequence having the lowestmetric. The MLSE is formally given by:{circumflex over (x)} =arg max _(x) {Pr( y|x )}.  (2)where

-   -   y denotes the received signal buffer;    -   x denotes the estimated sequence of symbols;

An equalizer employing Equation 2 above results in an estimate of atransmitted sequence of symbols which is most likely. This makes such anequalizer an efficient estimator. The conditional probability shown inthe equation, however, is unknown. A common assumption for calculatingthe conditional probability is that the noise is Additive White GaussianNoise (AWGN). In the case of GMSK co-channel interferers, however, anyassumption about the noise must take the GMSK transmitters into account.In accordance with the present invention, an extended model forcalculating this probability, and thus improving the equalizer'sperformance, is presented herein.

Metric Calculation and Decision Regions

For the AWGN channel, the probability distribution function of the noiseis given by $\begin{matrix}\begin{matrix}{{f_{N}(n)} = {\frac{1}{2{\pi\sigma}^{2}}{\exp\left\lbrack {- \frac{{n}^{2}}{2\sigma^{2}}} \right\rbrack}}} \\{= {\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\exp\left\lbrack {- \frac{{\mathcal{R}(n)}^{2}}{2\sigma^{2}}} \right\rbrack}\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\exp\left\lbrack {- \frac{{\mathcal{J}(n)}^{2}}{2\sigma^{2}}} \right\rbrack}}}\end{matrix} & (3)\end{matrix}$where

(n) and ℑ(n) denote the real and imaginary parts of a complex argument,respectively.

In other words, the noise is a complex Gaussian random variable withindependent components, each with a Gaussian distribution with zeroexpectation and variance of a σ². The conditional probability for theMLSE is given as: $\begin{matrix}\begin{matrix}{{\Pr\left( {\underset{\_}{y}\text{❘}\underset{\_}{x}} \right)} = {\Pr\left( {\underset{\_}{y}\text{❘}\underset{\_}{h}*\underset{\_}{x}} \right)}} \\{= {\Pr\left( {\underset{\_}{y}\text{❘}{\underset{\_}{x}}^{h}} \right)}} \\{= {\prod\limits_{i}\quad{\Pr\left( {y_{i}\text{❘}x_{i}^{h}} \right)}}} \\{= {\prod\limits_{i}{\frac{1}{2{\pi\sigma}^{2}}{\exp\left\lbrack \frac{{{y_{i} - x_{i}^{h}}}^{2}}{2\sigma^{2}} \right\rbrack}}}}\end{matrix} & (4)\end{matrix}$where x ^(h)=h*x is the vector of symbols x after passing through thechannel h, and * represents the convolution operator.

When taking the argmax, Equation 4 above can be simplified to thefollowing: $\begin{matrix}\begin{matrix}{\underset{\_}{\hat{x}} = {\arg\quad\max\left\{ {\prod\limits_{i}{\frac{1}{2{\pi\sigma}^{2}}{\exp\left\lbrack \frac{{{y_{i} - x_{i}^{h}}}^{2}}{2\sigma^{2}} \right\rbrack}}} \right\}}} \\{= {\arg\quad\max\left\{ {\prod\limits_{i}{\exp\left\lbrack \frac{{{y_{i} - x_{i}^{h}}}^{2}}{2\sigma^{2}} \right\rbrack}} \right\}}} \\{= {\arg\quad\max\left\{ {\sum\limits_{i}{- \frac{{{y_{i} - x_{i}^{h}}}^{2}}{2\sigma^{2}}}} \right\}}} \\{= {\arg\quad\min\left\{ {\sum\limits_{i}{{y_{i} - x_{i}^{h}}}^{2}} \right\}}} \\{= {\arg\quad\min\left\{ {{\underset{\_}{y} - {\underset{\_}{x}}^{h}}} \right\}}}\end{matrix} & (5)\end{matrix}$which leads to the well-known Minimum Euclidian Distance (MED)criterion. Note that calculating the metric for a given sequence doesnot require knowing the noise variance σ².

Every decision criterion imposes a division of the I/Q plane into eight(for 8PSK) decision regions, i.e. a mapping of every point on the I/Qplane to one of the eight symbols. The decision regions for the MEDcriterion are illustrated in FIG. 3. Note the regions are symmetric andevenly distributed around the origin with equal angles, distances, etc.due to the assumption of white noise being resulting in a square metric.

I/Q Correlated Noise

It is important to note that choosing the channel noise model to beGaussian with independent components may be convenient, but this is notalways the correct model. If the I and Q elements are correlated, as isthe case with GMSK interferers, it is possible to use this correlationto modify the decision rule, and improve the performance of theequalizer.

For defining the extended model, we mark the (complex) samples asvectors of 2 real elements: $\begin{matrix}{x = \begin{pmatrix}x^{R} \\x^{l}\end{pmatrix}} & (6)\end{matrix}$The probability distribution function of the noise is now defined by thefollowing: $\begin{matrix}\begin{matrix}{{{f_{N}(n)} = {\frac{11}{2\pi\sqrt{\Lambda }}{\exp\left\lbrack {{- \frac{1}{2}}n^{T}\Lambda^{- 1}n} \right\rbrack}}},{{where}\quad\Lambda}} \\{= {E\left( {n \cdot n^{T}} \right)}} \\{= {E\left( \begin{bmatrix}\left( n^{R} \right)^{2} & {n^{R}n^{l}} \\{n^{R}n^{l}} & \left( n^{l} \right)^{2}\end{bmatrix} \right)}}\end{matrix} & (7)\end{matrix}$where ∥•∥ denotes the determinant of the matrix in the argument. Thenoise presented above has the form of a Gaussian random vector with realcomponents which are possibly dependent. Each element in the noisevector obeys the zero mean Gaussian distribution law. Note that thismodel extends the previous model of Equation 3, which can be achieved bythe following substitution: $\begin{matrix}{\Lambda = {\begin{bmatrix}\sigma^{2} & 0 \\0 & \sigma^{2}\end{bmatrix}.}} & (8)\end{matrix}$

Using notation similar to the previous model, we get the following MLSEequation: $\begin{matrix}\begin{matrix}{\hat{\underset{\_}{x}} = {\arg\quad\max\left\{ {\Pr\left( {\underset{\_}{y}\text{❘}\underset{\_}{x}} \right)} \right\}}} \\{= {\arg\quad\max\left\{ {\prod\limits_{i}\quad{\Pr\left( {{\underset{\_}{y}}_{i}\text{❘}{\underset{\_}{x}}_{i}^{h}} \right)}} \right\}}} \\{= {\arg\quad\max\left\{ {\prod\limits_{i}\quad{\frac{1}{2\pi\sqrt{\Lambda }}{\exp\left\lbrack {{- \frac{1}{2}}\left( {y_{i} - x_{i}^{h}} \right)^{T}{\Lambda^{- 1}\left( {y_{i} - x_{i}^{h}} \right)}} \right\rbrack}}} \right\}}} \\{= {\arg\quad\min\left\{ {\sum\limits_{i}{\left( {y_{i} - x_{i}^{h}} \right)^{T}{\Lambda^{- 1}\left( {y_{i} - x_{i}^{h}} \right)}}} \right\}}}\end{matrix} & (9)\end{matrix}$In the case the noise is not correlated, Equation 9 collapses to theprevious metric of Equation 5.

Calculating the new metric requires knowledge of the noise covariancematrix Λ, which needs to be estimated, as described in more detailinfra. To illustrate the effect of an existing cross-correlation betweenin-phase and quadrature components of the noise, let us use for examplethe following covariance matrix $\Lambda = {\begin{bmatrix}1 & {.3} \\{.3} & 1\end{bmatrix}.}$The decision regions for the new decision rule which corresponds to thisexample Λ is shown in FIG. 4.

It is interesting to note that unlike the circular symmetric case whereeach decision region is bounded by only two straight lines the I/Qcorrelated scenario presented in FIG. 4 comprises few regions bounded bythree lines. Note also that another effect produced by the correlationof the noise is that the error rate for different symbols in theconstellation may now differ.

Rotation and Relation to Interference Cancellation

One assumption of the present invention is that the main (i.e. desired)signal is 8PSK, 3π/8 rotated while the interferer signal is GMSKmodulated with π/2 rotation. Adding signals of GMSK type and 3π/8shifted 8PSK results in a relative shift of π/8 rotation between themain signal and the interferer signal. In order to model the GMSKinterferer as correlated Gaussian noise, it is necessary to ‘rotate’ theinterferer correlation correspondingly (i.e. π/8 offset rotation).

The model is shown graphically in FIGS. 5 and 6. FIG. 5 is a diagramillustrating modeling an 8PSK signal with a BPSK interfering signal. Inthe model, generally referenced 500, an 8PSK transmitter 502 generatesan 8PSK signal to which a 3π/8 rotation is applied 504. A GMSKtransmitter 514 generates a BPSK signal to which an effective π/2rotation is applied 516. The signal from the main channel 506 andinterferer channel 518 are combined 508 and the combined received signalundergoes de-rotation 510 before being input to the 8PSK receiver 512.Note that upon receiving the buffer of received samples, the receiverde-rotates the samples by a factor of 3π/8 in order to remove anyrotation in the main signal. The interferer remains, however, rotated bya factor of π/8. This rotation must be considered both in estimating thecorrelation matrix and throughout the metric calculation process. Notealso that although the model fits best if the interferer channel isordered in the same direction (i.e. all elements of the FIR filter havethe same phase), it is still superior to the simpler assumption ofuncorrelated Gaussian noise. FIG. 6 is a diagram illustrating modelingof a GMSK interferer as rotated I/Q correlated noise. The I/Q correlatedGaussian noise is rotated by π/8 to yield the modeled interference.

It is important to note that although the invention is described in thecontext of a GMSK interferer, it is appreciated that the metricmodification described herein can be applied to other types ofinterferers, such as BPSK, QAM, or any interferer modulation exhibitingcorrelation in the I/Q plane, without departing from the scope of theinvention.

Estimating the Correlation Matrix

A block diagram illustrating an error vector calculation apparatus ascontemplated by the present invention used in canceling co-channelinterference is shown in FIG. 7. The block diagram depicts the metriccalculation portion of a receiver, generally referenced 700, andcomprises a de-rotated error vector calculator 702, correlation matrixestimator 704 and metric calculator 706. The resultant metric{circumflex over (x)} is used by the equalizer 708 in determining themost likely sequence of symbols transmitted. Note that blocks 702, 704,706 may be implemented within the equalizer or as a module externalthereto.

The correlation matrix is estimated from an error vector. The errorvector is estimated by subtracting the convolution of the known trainingsequence (TSC) symbols with the estimate of the channel from theoriginal received samples corresponding to the training sequence. Thisis expressed by the following:e=y−TRN*h   (10)wherein

-   -   e denotes the error vector;    -   y denotes the mid portion of the received buffer;    -   TRN represents the known training sequence;    -   h represents the estimated channel parameters vector;        Note that according to the model, the error vector e comprises        samples of the rotated Gaussian random vector n, and hence needs        to be de-rotated. In addition, the particular channel estimation        h used is not critical to the invention. The de-rotated error        vector {tilde over (e)} is defined as follows: $\begin{matrix}        {{\overset{\sim}{e}}_{n} = {e_{n} \cdot {\exp\left( {{- j}\frac{\pi}{8}n} \right)}}} & (11)        \end{matrix}$        The de-rotated error vector {tilde over (e)} is a vector of        samples of the random vector n, and the estimation of        $\Lambda = {E\left( \begin{bmatrix}        \left( n^{R} \right)^{2} & {n^{R}n^{l}} \\        {n^{R}n^{l}} & \left( n^{l} \right)^{2}        \end{bmatrix} \right)}$        can be done in a straight-forward fashion by averaging:        $\begin{matrix}        {\Lambda_{11} = {{E\left( \left( n^{R} \right)^{2} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}}} & (12) \\        {{\Lambda_{22}{E\left( \left( n^{l} \right)^{2} \right)}} \approx {\frac{1}{N - 1}{{{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}} & (13) \\        {\Lambda_{12} = {\Lambda_{21} = {{E\left( {n^{R}n^{l}} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}}}} & (14)        \end{matrix}$        where N is the length of {tilde over (e)}.

Determining the Correct Correlation Matrix

The expression for the MLSE shown above in Equation 9 assumes that theadditive noise has a given correlation matrix which remains constantover time. In the modified model of the present invention which includesa rotation factor, the correlation of the noise in each received sampledepends on the particular sample index, as follows:

For sample k, the additive noise is expressed as $\begin{matrix}{n_{k} = {n \cdot {\exp\left( j^{\frac{\pi\quad k}{8}} \right)}}} & (15)\end{matrix}$

For a vector representation of the noise (noted by a bold n), the noisen_(k) and the correlation are given by the following $\begin{matrix}\begin{matrix}{n_{k} = \begin{bmatrix}{{Re}\left( n_{k} \right)} \\{{Im}\left( n_{k} \right)}\end{bmatrix}} \\{= {{\begin{bmatrix}{\cos\left( \frac{\pi\quad k}{8} \right)} & {- {\sin\left( \frac{\pi\quad k}{8} \right)}} \\{\sin\left( \frac{\pi\quad k}{8} \right)} & {\cos\left( \frac{\pi\quad k}{8} \right)}\end{bmatrix} \cdot n}\hat{=}{\Phi_{k} \cdot n}}}\end{matrix} & (16) \\\begin{matrix}{\Lambda_{k} = {E\left( {n_{k} \cdot n_{k}^{T}} \right)}} \\{= {E\left( {\Phi_{k}{n \cdot \left( {\Phi_{k}n} \right)^{T}}} \right)}} \\{= {E\left( {\Phi_{k}{n \cdot n^{T}}\Phi_{k}^{T}} \right)}} \\{= {\Phi_{k}{E\left( {n \cdot n^{T}} \right)}\Phi_{k}^{T}}} \\{= {\Phi_{k}\Lambda\quad\Phi_{k}^{T}}}\end{matrix} & (17)\end{matrix}$where

-   -   Λ_(k) is the time varying correlation matrix for a correlated        signal after rotation;    -   Λ is the correlation matrix before rotation;    -   Φ_(k) is the rotation matrix;

Therefore, for the sample at time k, the correlation matrix for thecalculation of the metric should be Λ_(k)=Φ_(k)ΛΦ_(k) ^(T) and not theoriginal Λ described supra. The extension to the model presented hereresults in a corrected version of the MLSE equations presented above,as: $\begin{matrix}{\underset{\_}{\hat{x}} = {\arg\quad\min\left\{ {\sum\limits_{k}{\left( {y_{k} - x_{k}^{h}} \right)^{T}{\Lambda_{k}^{- 1}\left( {y_{k} - x_{k}^{h}} \right)}}} \right\}}} & (18)\end{matrix}$The following is used to calculate the metric of an equalization errorat time k: $\begin{matrix}\begin{matrix}{{Metric} = {n^{T} \cdot \Lambda^{- 1} \cdot n}} \\{= {\left( {\Phi_{k}^{T}\Phi_{k}n} \right)^{T}{\Lambda^{- 1}\left( {\Phi_{k}^{T}\Phi_{k}n_{k}} \right)}}} \\{= {\left( {\Phi_{k}n} \right)^{T}\Phi_{k}\Lambda^{- 1}{\Phi_{k}^{T}\left( {\Phi_{k}n_{k}} \right)}}} \\{= {\left( {\Phi_{k}n} \right)^{T}{\Lambda_{k}^{- 1}\left( {\Phi_{k}n_{k}} \right)}}} \\{= {n_{k}^{T}\Lambda_{k}^{- 1}n_{k}}}\end{matrix} & (19)\end{matrix}$

One may observe that the model correction proposed here is expressed interms of a time varying correlation matrix denoted by Λ_(k). Thedecision regions for rotated correlation matrices Λ=Λ₀ and its rotationsΛ_(k) for k=0, 1, . . . , 7 are shown in FIGS. 8A through 8H,respectively.

Performance Gain

Simple simulations (i.e. additive noise, single-tap channel) show theaverage gain achieved from using the correct correlation matrix. In thepresented simulation we select noise correlation matrices of the form${\Lambda = \begin{bmatrix}1 & ɛ \\ɛ & 1\end{bmatrix}};$where ε˜U[0,1]. In addition, the correlation matrices are rotated in anangle chosen uniformly from$\left\{ {0,\frac{\pi}{8},\frac{2\pi}{8},\ldots\quad,\frac{7\pi}{8}} \right\}.$The simulation results are shown in FIG. 9 which is a graph illustratingsymbol error rate (SER) versus SNR when using the correct correlationmatrix for correlated noise.

Implementation Notes

Considering the following characteristic of the rotation matrix:$\begin{matrix}\begin{matrix}{\Phi_{k + 8} = \begin{bmatrix}{\cos\left( \frac{\pi\left( {k + 8} \right)}{8} \right)} & {- {\sin\left( \frac{\pi\left( {k + 8} \right)}{8} \right)}} \\{\sin\left( \frac{\pi\left( {k + 8} \right)}{8} \right)} & {\cos\left( \frac{\pi\left( {k + 8} \right)}{8} \right)}\end{bmatrix}} \\{= \begin{bmatrix}{\cos\left( {\frac{\pi\quad k}{8} + \pi} \right)} & {- {\sin\left( {\frac{\pi\quad k}{8} + \pi} \right)}} \\{\sin\left( {\frac{\pi\quad k}{8} + \pi} \right)} & {\cos\left( {\frac{\pi\quad k}{8} + \pi} \right)}\end{bmatrix}} \\{= {- \begin{bmatrix}{\cos\left( \frac{\pi\quad k}{8} \right)} & {- {\sin\left( \frac{\pi\quad k}{8} \right)}} \\{\sin\left( \frac{\pi\quad k}{8} \right)} & {\cos\left( \frac{\pi\quad k}{8} \right)}\end{bmatrix}}} \\{= {- \Phi_{k}}}\end{matrix} & (20)\end{matrix}$

results in the following expression for the correlation matrix:Λ_(k+8)=Φ_(k+8)ΛΦ_(k+8) ^(T)=[−Φ_(k)]Λ[−Φ_(k)]^(T)=Φ_(k)ΛΦ_(k)^(T)=Λ_(k)  (21)The relation above implies that Λ_(k) is cyclic with only eight relevantmatrices which may be calculated a priori before the equalizer ratherthan needing to be calculated at each equalizer step.

It is important to note that the model presented above is for anequalizer which is placed after a whitening matched filter (WMF)process. This implies that that correlation estimates are performedtwice during each burst, i.e. once for the left side of the burst andonce for the right side of the burst.

Per-Survivor Equalization Error Prediction (PSP)

When the correlated noise model of the present invention is considered,other modules within or external to the equalizer may need to beextended to incorporate the new metric. One such process is the PSPwhitening process, which is described in more detail below.

Similarly to the above described metric with I/Q correlation, we mayalso consider temporal error correlation. This effect may be modeled asa correlation between consecutive samples of the error signal. Thetemporal correlation extends the interference signal model, while beingrelatively simple in terms of receiver resources and which alsopreserves the blind receiver attribute. Applying this notion to anequalization process is conventionally termed PSP (per survivorprocessing) but can also be considered an ‘equalization error reductionalgorithm’.

Consider a simple model for the equalization path error process asfollows:n _(k) =c·n _(k−1) +w _(k)  (22)where

n_(k) denotes the error process;

c represents a complex scalar;

w_(k) is WSS white complex Gaussian process;

The error process defined above is commonly termed a first orderauto-regressive process. It is clear that under the model presented,having c and n_(k−1) may reduce the residual error from n_(k) to w_(k).

In operation, n_(k−1) is derived during equalization, while c isestimated. In addition, one may use two models for the error signal. Thefirst model is used for a main signal and an interfering signal withsimilar angle of rotation. This case appears in GMSK/GMSK and 8PSK/8PSKscenarios. The second model is used where the main signal and theinterfering signals have an offset in their angle of rotation. Thesecases are denoted GMSK/8PSK and 8PSK/GMSK accordingly. Preferably, thetwo different cases are treated separately.

Assuming that the existence of an offset in the rotation angle is knownto the modem in both cases, it is then required to have an un-rotatederror process. Taking the error samples measured over the TSC, one mayestimate c using the following equation: $\begin{matrix}{\hat{c} = \frac{{\hat{R}}_{n,n}\lbrack 1\rbrack}{{\hat{R}}_{n,n}\lbrack 0\rbrack}} & (23)\end{matrix}$

The equation for ĉ corresponds both to a Yule-Walker equationformulation and to an LS approach. The difference between the twoapproaches is that $\begin{matrix}{{{R_{n,n}^{YW}\lbrack 0\rbrack} = {\frac{1}{N}{\sum\limits_{i = 1}^{N}{n_{i}}^{2}}}}{and}} & (24) \\{{R_{n,n}^{LS}\lbrack 0\rbrack} = {\frac{1}{N - 1}{\sum\limits_{i = 1}^{N - 1}{{n_{i}}^{2}.}}}} & (25)\end{matrix}$For both cases $\begin{matrix}{{R_{n,n}\lbrack 1\rbrack} = {\frac{1}{N - 1}{\sum\limits_{i = 1}^{N - 1}{n_{i} \cdot {n_{i + 1}^{*}.}}}}} & (26)\end{matrix}$

For both cases presented above the change in the error process modelrequires a correction to the error correlation matrix. This is becauseof the need to properly calculate the new error process according to thefollowing equationŵ _(k) =n _(k) −ĉ·n _(k−1).  (27)

First, we write w and n for noting the vector form:${x = {{\begin{pmatrix}x^{R} \\x^{l}\end{pmatrix}\quad{and}\quad w} = \begin{pmatrix}w^{R} \\w^{l}\end{pmatrix}}},$getting: $\begin{matrix}\begin{matrix}{w_{k} = \begin{pmatrix}w_{k}^{R} \\w_{k}^{l}\end{pmatrix}} \\{= {\begin{pmatrix}n_{k}^{R} \\n_{k}^{l}\end{pmatrix} - \begin{pmatrix}\left\lbrack {\hat{c} \cdot n_{k - 1}} \right\rbrack^{R} \\\left\lbrack {\hat{c} \cdot n_{k - 1}} \right\rbrack^{l}\end{pmatrix}}} \\{= {\begin{pmatrix}n_{k}^{R} \\n_{k}^{l}\end{pmatrix} - \begin{pmatrix}{{{\hat{c}}^{R} \cdot n_{k - 1}^{R}} - {{\hat{c}}^{l} \cdot n_{k - 1}^{l}}} \\{{{\hat{c}}^{R} \cdot n_{k - 1}^{l}} + {{\hat{c}}^{l} \cdot n_{k - 1}^{R}}}\end{pmatrix}}} \\{= {\begin{pmatrix}n_{k}^{R} \\n_{k}^{l}\end{pmatrix} - {\overset{\overset{\hat{c}}{︷}}{\begin{pmatrix}{\hat{c}}^{R} & {- {\hat{c}}^{l}} \\{\hat{c}}^{l} & {\hat{c}}^{R}\end{pmatrix}}\begin{pmatrix}n_{k - 1}^{R} \\n_{k - 1}^{l}\end{pmatrix}}}} \\{= {n_{k} - {\hat{C} \cdot n_{k - 1}}}}\end{matrix} & (28)\end{matrix}$

The new error process (ŵ_(k)) correlation matrix is derived as follows:$\begin{matrix}\begin{matrix}{\Lambda_{k} = {E\left( {w_{k} \cdot w_{k}^{T}} \right)}} \\{= {E\left( {\left( {n_{k} - {\hat{C} \cdot n_{k - 1}}} \right) \cdot \left( {n_{k} - {\hat{C} \cdot n_{k - 1}}} \right)^{T}} \right)}} \\{= {\Lambda - {2 \cdot \hat{C} \cdot {E\left( {n_{k - 1} \cdot n_{k}^{T}} \right)}} + {\hat{C} \cdot \Lambda \cdot {\hat{C}}^{T}}}} \\{= {\Lambda - {\hat{C} \cdot \Lambda \cdot {\hat{C}}^{T}}}}\end{matrix} & (29)\end{matrix}$where the last equation is from:E(n _(k−1) ·n _(k) ^(T))=E(n _(k−1)·(Ĉ·n _(k−1) +w _(k))^(T))=E(n _(k−1)·n _(k−1) ^(T) ·Ĉ ^(T) +n _(k−1) w _(k) ^(T))=Λ·Ĉ ^(T)+0=Λ·Ĉ ^(T)  (30)It can be observed that the process of noise prediction reduces thevariance (and I/Q covariance) of the equalization error.

Extending the Model: Optimal Linear Predictor

By referring to the signals (noise and main signals) as vectors ratherthan complex numbers, the model of equalization error prediction can beextended in the following manner. The vector n_(k) is predicted using{circumflex over (n)}_(k)=C·n_(k−1), where the predicting matrix C, isnot necessarily a matrix representing a complex number (i.e. a matrix Cwhere C₁₁=C₂₂; C₁₂=−C₂₁). The optimal predicting matrix using a minimummean square error (MMSE) technique is used to achieve the minimum meansquare error (i.e. variance and I/Q covariance) as follows.

The well-known MMSE optimal linear estimator for a vector x out of thevector y is give by{circumflex over (x)}=C _(XY) ·C _(YY) ⁻¹ ·y   (31)and the mean square error is given byMSE=C _(XX) −C _(XY) ·C _(YY) ⁻¹ ·C _(YX)  (32)Translating the estimator and the mean squared error (MSE) equationsyields the following.Estimating n_(k) out of n_(k−1):A{circumflex over (=)}C _(n) _(k) _(n) _(k) =E[n _(k) n _(k) ^(T) ]=E[n_(k−1) n _(k−1) ^(T)]  (33)B{circumflex over (=)}C _(n) _(k) _(n) _(k−1) =E[n _(k) n _(k−1)^(T)]  (34)The optimal prediction matrix isC{circumflex over (=)}C _(n) _(k) _(n) _(k−1) C _(n) _(k) _(n) _(k) ⁻¹=BA ⁻¹  (34)while the MSE is defined as Λ=A−BA⁻¹B^(T). Note that the MSE is exactlythe correlation matrix of the residual noise w_(k) that fits into themodel as follows:MSE=E└({circumflex over (n)} _(k) −n _(k))({circumflex over (n)} _(k) −n_(k))^(T) ┘=E└(C·n _(k−1) −n _(k))(C·n _(k−1) −n _(k))^(T) ┘=E[w _(k) w_(k) ^(T)]=Λ  (35)

In order to estimate the prediction matrices A, B and C, we estimate thecorrelation values in the same manner as above: $\begin{matrix}{{{{A_{11} = {{E\left( \left( n_{k}^{R} \right)^{2} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}}};}A_{22} = {{E\left( \left( n_{k}^{l} \right)^{2} \right)} \approx {\frac{1`}{N - 1}{{{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}}}{A_{12} = {A_{21} = {{E\left( {n_{k}^{R}n_{k}^{l}} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}}}}}}} & (36) \\{{{B_{11} = {{E\left( {n_{k}^{R}n_{k - 1}^{R}} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Re}\left( \underset{\_}{\overset{\Cap}{e}} \right)}}}}};}{B_{22} = {{E\left( {n_{k}^{l}n_{k - 1}^{l}} \right)} \approx {\frac{1}{N - 1}{{{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\Cap}{e}} \right)}}}}}{{B_{12} = {{E\left( {n_{k}^{R}n_{k - 1}^{l}} \right)} \approx {\frac{1}{N - 1}{{{Re}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Im}\left( \underset{\_}{\overset{\Cap}{e}} \right)}}}}};}{B_{21} = {{E\left( {n_{k}^{l}n_{k - 1}^{R}} \right)} \approx {\frac{1}{N - 1}{{{Im}\left( \underset{\_}{\overset{\sim}{e}} \right)}^{T} \cdot {{Re}\left( \underset{\_}{\overset{\Cap}{e}} \right)}}}}}} & (37)\end{matrix}$where

is the vector {tilde over (e)} with a shift of one symbol ‘backwards’:

_(k)={tilde over (e+ )}

The implications on the metric calculation will now be discussed. Givensamples of equalization errors ñ_(k) and ñ_(k−1), we need to calculatethe metric for a given decision. Note that ñ_(k) is a sample of theequalization noise, without de-rotation, while n_(k) is de-rotated.Recalling that $\begin{matrix}{\Phi_{k}\overset{\bigwedge}{=}\begin{bmatrix}{\cos\left( \frac{\pi\quad k}{8} \right)} & {- {\sin\left( \frac{\pi\quad k}{8} \right)}} \\{\sin\left( \frac{\pi\quad k}{8} \right)} & {\cos\left( \frac{\pi\quad k}{8} \right)}\end{bmatrix}} & (38)\end{matrix}$we note that ñ_(k){circumflex over (=)}Φ_(−k)n_(k) which yields thefollowing:w _(k) =n _(k) −C·n _(k−1)=Φ_(k) ñ _(k) −C·Φ _(k−1) ñ _(k−1).  (39)The following is used to calculate the metric of an equalization errorat time k: $\begin{matrix}\begin{matrix}{{Metric} = {w_{k}^{T} \cdot \Lambda^{- 1} \cdot w_{k}}} \\{= {\left( {{\Phi_{k}{\overset{\sim}{n}}_{k}} - {C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)^{T}{\Lambda^{- 1}\left( {{\Phi_{k}{\overset{\sim}{n}}_{k}} - {C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)}}} \\{= {\left( {{\Phi_{k}{\overset{\sim}{n}}_{k}} - {\Phi_{k}\Phi_{- k}C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)^{T}{\Lambda^{- 1}\left( {{\Phi_{k}{\overset{\sim}{n}}_{k}} - {\Phi_{k}\Phi_{- k}C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)}}} \\{= {\left( {{\overset{\sim}{n}}_{k} - {\Phi_{- k}C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)^{T}\Phi_{k}^{T}\Lambda^{- 1}{\Phi_{k}\left( {{\overset{\sim}{n}}_{k} - {\Phi_{- k}C\quad\Phi_{k - 1}{\overset{\sim}{n}}_{k - 1}}} \right)}}} \\{= {\left( {{\overset{\sim}{n}}_{k} - {\Phi_{- k}C\quad\Phi_{- 1}\Phi_{k}{\overset{\sim}{n}}_{k - 1}}} \right)^{T}\Phi_{k}^{T}\Lambda^{- 1}{\Phi_{k}\left( {{\overset{\sim}{n}}_{k} - {\Phi_{- k}C\quad\Phi_{- 1}\Phi_{k}{\overset{\sim}{n}}_{k - 1}}} \right)}}}\end{matrix} & (40)\end{matrix}$The final expression for the metric thus includes consideration forrotation, I/Q correlation and temporal error correlation. The metric nowdepends on the expressions: ñ_(k), ñ_(k−1), which are provided in theequalization process along with Φ_(−k)CΦ⁻¹Φ_(k), Φ_(k) ^(T)Λ⁻¹Φ_(k).Note that these last two expressions are pre-calculated and stored in alookup table as described in connection with Equation 21 supra.

Soft Value Generation

Note that modifying the metric model to one that takes intoconsideration additive noise with correlated in phase and quadrature(I/Q) elements changes the conditional probability Pr(y)}|x). The firstchange, as described above, is made in the way the equalizer selects thesurviving path, i.e. the metric according to the present invention. Ifsoft symbols or bits are to be generated, the soft value generator (SVG)within the receiver is modified accordingly. The soft values are in factlog of likelihood rates which rely heavily on Pr(y|x). Changes to theSVG are described in more detail hereinbelow.

As described supra, the hard decisions output by the equalizer representthe most likely series of symbols. One way to improve the performance ofthe receiver is to associate soft values to the hard decisions. The softvalue of an equalizer output bit is the log of the likelihood ratio(LLR) for that bit which provides a measure of how ‘strong’ thecorresponding hard decision is. The backend outer decoder uses the softvalue information to improve decoding of the information bits.

The soft values rely on the hard decisions generated by the equalizer.Thus, the soft value generator is a post decision module. The soft valuecorresponding to a specific bit may be found by deriving the LLR oferror probabilities for that specific bit: $\begin{matrix}{{{LLR}\left( {b_{j} = 1} \right)} = {\ln\frac{P\left( {{\underset{\_}{y}\text{❘}b_{j}} = 1} \right)}{P\left( {{\underset{\_}{y}\text{❘}b_{j}} = 0} \right)}}} & (41)\end{matrix}$The above presented log-likelihood-ratio can be represented in terms ofthe symbol LLR as: $\begin{matrix}{{{{{LLR}\left( {b_{j} = 1} \right)} = {{\ln\left\lbrack {\sum\limits_{l \in D_{j\quad 1}}{\mathbb{e}}^{{LLR}{({S_{k} = A_{l}})}}} \right\rbrack} - {\ln\left\lbrack {\sum\limits_{l \in D_{j\quad 0}}{\mathbb{e}}^{{LLR}{({S_{k} = A_{l}})}}} \right\rbrack}}};}{{{LLR}\left( {S_{k} = A_{l}} \right)} = {\ln\frac{P\left( {{\underset{\_}{y}\text{❘}S_{k}} = A_{l}} \right)}{P\left( {{\underset{\_}{y}\text{❘}S_{k}} = A_{0}} \right)}}}} & (42)\end{matrix}$where

-   -   S_(k) is the k^(th) symbol decision;    -   A_(l) is the symbol value;    -   A₀ is the reference symbol value;    -   b_(j) is the bit value for the j^(th) bit of the symbol;    -   D_(j0), D_(j1) represents the set of symbols in which b_(j)=0        and 1, respectively;        In order to reduce complexity while maintaining performance, the        following approximation is used: $\begin{matrix}        {{{{\ln\left\lbrack {\sum\limits_{l \in D_{j\quad 0}}{\mathbb{e}}^{{LLR}{({S_{k} = A_{l}})}}} \right\rbrack} \approx {\max\underset{l \in D_{j\quad 0}}{\left\lbrack {{LLR}\left( {S_{k} = A_{l}} \right)} \right\rbrack}\quad b}} = 0},1} & (43)        \end{matrix}$        The symbol that makes this approximation valid may be found from        a table generated a priori.

We assume that during the LLR calculation of the k^(th) symbol, all theother symbols in S (i.e. the hard decision vector) are free of decisionerrors. Therefore we may use the following expression: $\begin{matrix}{{\ln\frac{P\left( {{\underset{\_}{y}\text{❘}S_{k}} = A_{l}} \right)}{P\left( {{\underset{\_}{y}\text{❘}S_{k}} = A_{0}} \right)}} = {\ln\frac{P\left( {\underset{\_}{y}\text{❘}\underset{\_}{\hat{S}}} \right)}{P\left( {\underset{\_}{y}\text{❘}\underset{\_}{S}} \right)}}} & (44)\end{matrix}$where is the vector S, with a change only in the k^(th) symbol. Let S^(h)=h*S denote x ^(h) for the sake of clarity. $\begin{matrix}\begin{matrix}{{\Pr\left( {\underset{\_}{y}\text{❘}{\underset{\_}{S}}^{h}} \right)} = {\prod\limits_{i}\quad{\Pr\left( {y_{i}\text{❘}S_{i}^{h}} \right)}}} \\{= {\prod\limits_{i}\quad{\frac{1}{2\quad\pi\quad\sigma^{2}}{{\exp\left\lbrack {- \frac{{{y_{i} - S_{i}^{h}}}^{2}}{2\sigma^{2}}} \right\rbrack}.}}}}\end{matrix} & (45) \\\begin{matrix}{{\ln\frac{P\left( {\underset{\_}{y}\text{❘}\hat{\underset{\_}{S}}} \right)}{P\left( {\underset{\_}{y}\text{❘}\underset{\_}{S}} \right)}} = {\ln\frac{\Pr\left( {\underset{\_}{y}\text{❘}\underset{\_}{h}*\hat{\underset{\_}{S}}} \right)}{\Pr\left( {\underset{\_}{y}\text{❘}\underset{\_}{h}*\underset{\_}{S}} \right)}}} \\{= {\ln\frac{\Pr\left( {\underset{\_}{y}\text{❘}{\hat{\underset{\_}{S}}}^{h}} \right)}{\Pr\left( {\underset{\_}{y}\text{❘}{\underset{\_}{S}}^{h}} \right)}}} \\{= {\ln\frac{\prod\limits_{i}\quad{\Pr\left( {y_{i}\text{❘}{\hat{S}}_{i}^{h}} \right)}}{\prod\limits_{i}\quad{\Pr\left( {y_{i}\text{❘}S_{i}^{h}} \right)}}}} \\{= {\ln\frac{\prod\limits_{i}\quad{\frac{1}{2\quad\pi\quad\sigma^{2}}{\exp\left\lbrack {- \frac{{{y_{i} - {\hat{S}}_{i}^{h}}}^{2}}{2\quad\sigma^{2}}} \right\rbrack}}}{\prod\limits_{i}\quad{\frac{1}{2\quad\pi\quad\sigma^{2}}{\exp\left\lbrack {- \frac{{{y_{i} - {\hat{S}}_{i}^{h}}}^{2}}{2\quad\sigma^{2}}} \right\rbrack}}}}} \\{= {{\ln\left\lbrack {\prod\limits_{i}{\exp\left\lbrack {- \frac{{{y_{i} - {\hat{S}}_{i}^{h}}}^{2}}{2\quad\sigma^{2}}} \right\rbrack}} \right\rbrack} - {\ln\left\lbrack {\prod\limits_{i}{\exp\left\lbrack {- \frac{{{y_{i} - S_{i}^{h}}}^{2}}{2\quad\sigma^{2}}} \right\rbrack}} \right\rbrack}}} \\{= {{\frac{1}{2\quad\sigma^{2}}{\sum\limits_{i}{{y_{i} - S_{i}^{h}}}}} - {\frac{1}{2\quad\sigma^{2}}{\sum\limits_{i}{{y_{i} - {\hat{S}}_{i}^{h}}}^{2}}}}}\end{matrix} & (46)\end{matrix}$One may observe that

and S differ only in their k^(th) symbol,

^(h) and S^(h) differ only in symbols j; k≦j≦k+L−1. According to thisobservation the summation is effected only over the channel length −L asfollows: $\begin{matrix}{{\ln\frac{P\left( {\underset{\_}{y}\text{❘}\hat{\underset{\_}{S}}} \right)}{P\left( {\underset{\_}{y}\text{❘}\underset{\_}{S}} \right)}} = {{\frac{1}{2\quad\sigma^{2}}{\sum\limits_{i = k}^{k + L - 1}{{y_{i} - S_{i}^{h}}}^{2}}} - {\frac{1}{2\quad\sigma^{2}}{\sum\limits_{i = k}^{k + L - 1}{{y_{i} - {\hat{S}}_{i}^{h}}}^{2}}}}} & (47)\end{matrix}$Using the notation: y_(i)−S_(i) ^(h)=e_(i),y_(i)−

_(i) ^(h)=

_(i), where e_(i) and

_(i) are complex numbers, the following relation holds: $\begin{matrix}{{\ln\frac{P\left( {{\underset{\_}{y}❘S_{k}} = A_{l}} \right)}{P\left( {{\underset{\_}{y}❘S_{k}} = A_{0}} \right)}} = {\frac{1}{2\sigma^{2}}\left( {{\sum\limits_{i}{e_{i}}^{2}} - {{\hat{e}}_{i}}^{2}} \right)}} & (48) \\{\left. {{Therefore}\text{:}}\Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {{\max\limits_{l \in D_{j\quad 1}}\left( {{LLR}\left( {s_{k} = A_{l}} \right)} \right)} - {\max\limits_{l \in D_{j\quad 0}}\left( {{LLR}\left( {s_{k} = A_{l}} \right)} \right)}}} \right. = {{{\max\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2\sigma^{2}}\left( {{\sum\limits_{i}{e_{i}}^{2}} - {{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)} - {\max\limits_{l \in D_{j\quad 0}}\left( {\frac{1}{2\quad\sigma^{2}}\left( {{\sum\limits_{i}{e_{i}}^{2}} - {{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)}} = {{{\max\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2\sigma^{2}}\left( {\sum\limits_{i}{- {{\overset{\Cap}{e}}_{i,l}}^{2}}} \right)} \right)} - {\max\limits_{l \in D_{j\quad 0}}\left( {\frac{1}{2\quad\sigma^{2}}\left( {\sum\limits_{i}{- {{\overset{\Cap}{e}}_{i,l}}^{2}}} \right)} \right)}} = {{\min\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2\sigma^{2}}\left( {\sum\limits_{i}{{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)} - {\min\limits_{l \in D_{j\quad 0}}\left( {\frac{1}{2\quad\sigma^{2}}\left( {\sum\limits_{i}{{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)}}}}} & (49)\end{matrix}$The expression$\min\limits_{l \in D_{j\quad 0}}\left( {\frac{1}{2\quad\sigma^{2}}\left( {\sum\limits_{i}{{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)$is obtained directly from the equalizer hard-decisions. Since theequalizer performs a minimization of the error (Euclidian) metric nominimum operation is needed for this part of the expression above.$\begin{matrix}{\left. \Rightarrow\quad{{{LLR}\left( {b_{j} = 1} \right)} \approx {{\min\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2\quad\sigma^{2}}\left( {\sum\limits_{i}{{\overset{\Cap}{e}}_{i,l}}^{2}} \right)} \right)} - {\frac{1}{2\sigma^{2}}{\sum\limits_{i}{e_{i}^{eq}}^{2}}}}} \right. = {\min\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2\sigma^{2}}\left( {{\sum\limits_{i}{{\overset{\Cap}{e}}_{i,l}}^{2}} - {e_{i}^{eq}}^{2}} \right)} \right)}} & (50) \\{{\overset{\Cap}{e}}_{i} = {{y_{i} - {\overset{\Cap}{S}}_{i}^{h}} = {{y_{i} - {{\overset{\Cap}{S}}_{i}*h}} = {y_{i} - {\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot {{\overset{\Cap}{S}}_{i - n}.}}}}}}} & (51)\end{matrix}$Assuming an error only in the k^(th) symbol, and 0≦i−k<L, i−k=Δ,$\begin{matrix}\begin{matrix}{{\overset{\Cap}{e}}_{i} = {y_{i} - {\sum\limits_{{n = 0},{n \neq \Delta}}^{L - 1}{h_{n} \cdot {\overset{\Cap}{S}}_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}}}} \\{= {y_{i} - {\sum\limits_{{n = 0},{n \neq \Delta}}^{L - 1}{h_{n} \cdot {\overset{\Cap}{S}}_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}} + {h_{\Delta} \cdot S_{i - \Delta}} - {h_{\Delta} \cdot S_{i - \Delta}}}}\end{matrix} & (52)\end{matrix}$Since

and S differ only by their k^(th) symbols: $\begin{matrix}{{y_{i} - {\sum\limits_{{n = 0},{n \neq \Delta}}^{L - 1}{h_{n} \cdot S_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}} + {h_{\Delta} \cdot S_{i - \Delta}} - {h_{\Delta} \cdot S_{i - \Delta}}} = {y_{i} - {\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot S_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}} + {h_{\Delta} \cdot S_{i - \Delta}}}} & (53) \\{{e_{i}^{eq} - {h_{\Delta} \cdot \left( {{\overset{\Cap}{S}}_{i - \Delta} - S_{i - \Delta}} \right)}} = {{e_{i}^{eq} - {{h_{\Delta} \cdot \Delta}\quad S}} = {\overset{\Cap}{e}}_{i}}} & (54) \\\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2\sigma^{2}} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L - 1}{{e_{i}^{eq} - {{h_{i} \cdot \Delta}\quad S_{l}}}}^{2}} - {e_{i}^{eq}}^{2}} \right)}}} \right. & (55)\end{matrix}$

The soft value generation process, including the generation of softsymbols values, conversion of soft symbols to soft bits and a symbolcompetitor algorithm, is described in more detail in the following: U.S.Pat. No. 6,731,700, entitled “Soft Decision Output Generator,” U.S. Pat.No. 6,944,242, entitled “Apparatus For And Method Of Converting SoftSymbol Information To Soft Bit Information,” and U.S. Pat. No.6,529,559, entitled “Reduced Soft Output Information Packet Selection,”all of which are hereby incorporated herein by reference in theirentirety.

As an example of the benefit of the soft value generator, a trellisdiagram illustrating the effect of a competitor symbol on the cumulativemetric calculation is shown in FIG. 10 for a channel length of L−1. Themaximum likelihood path is shown as the solid trace while the competingpath is shown as the dashed trace.

Model Extension 1: De-Correlation

As described supra in the section entitled “I/Q Correlated Noise”, theinput samples are marked as vectors of two real elements:$\begin{matrix}{x = {\begin{pmatrix}x^{R} \\x^{l}\end{pmatrix}.}} & \left( {{Equation}\quad 6} \right)\end{matrix}$Since the noise probability distribution function is defined by:$\begin{matrix}{{{f_{N}(n)} = {\frac{1}{2\pi\sqrt{\Lambda }}{\exp\left\lbrack {{- \frac{1}{2}}n^{T}\Lambda^{- 1}n} \right\rbrack}}}{where}} & (56) \\{\Lambda = {{E\left( {n \cdot n^{T}} \right)} = {E\left( \begin{bmatrix}\left( n^{R} \right)^{2} & {n^{R}n^{l}} \\{n^{l}n^{R}} & \left( n^{l} \right)^{2}\end{bmatrix} \right)}}} & (57) \\{{{\ln\frac{P\left( {\underset{\_}{y}\text{❘}\overset{\Cap}{\underset{\_}{S}}} \right)}{P\left( {\underset{\_}{y}\text{❘}\underset{\_}{S}} \right)}} = {{{\ln\left\lbrack {\prod\limits_{i}\quad{\exp\left\lbrack {{{- \frac{1}{2}} \cdot \left\lbrack {{\underset{\_}{y}}_{i} - {\overset{\Cap}{\underset{\_}{S}}}_{i}^{h}} \right\rbrack^{T}}{\Lambda^{- 1}\left\lbrack {{\underset{\_}{y}}_{i} - {\overset{\Cap}{\underset{\_}{S}}}_{i}^{h}} \right\rbrack}} \right\rbrack}} \right\rbrack} - {\ln\left\lbrack {{\prod\limits_{i}\quad\exp} - {{\frac{1}{2} \cdot \left\lbrack {{\underset{\_}{y}}_{i} - {\underset{\_}{S}}_{i}^{h}} \right\rbrack^{T}}{\Lambda^{- 1}\left\lbrack {{\underset{\_}{y}}_{i} - {\underset{\_}{S}}_{i}^{h}} \right\rbrack}}} \right\rbrack}} = {{\frac{1}{2}{\sum\limits_{i = k}^{k + L - 1}{\left\lbrack {{\underset{\_}{y}}_{i} - {\overset{\Cap}{\underset{\_}{S}}}_{i}^{h}} \right\rbrack^{T}{\Lambda^{- 1}\left\lbrack {{\underset{\_}{y}}_{i} - {\overset{\Cap}{\underset{\_}{S}}}_{i}^{h}} \right\rbrack}}}} - {\frac{1}{2}{\sum\limits_{i = k}^{k + L - 1}{\left\lbrack {{\underset{\_}{y}}_{i} - {\underset{\_}{S}}_{i}^{h}} \right\rbrack^{T}{\Lambda^{- 1}\left\lbrack {{\underset{\_}{y}}_{i} - {\underset{\_}{S}}_{i}^{h}} \right\rbrack}}}}}}}{where}} & (58) \\{{\underset{\_}{S}}_{i}^{h} = {\sum\limits_{n = 0}^{L - 1}{H_{i} \cdot {\underset{\_}{S}}_{i - n}}}} & (59)\end{matrix}$and H_(i) is the i^(th) tap of the channel vector h in a matrix form:$\begin{matrix}{{H_{i} = \begin{bmatrix}h_{i}^{R} & {- h_{i}^{l}} \\h_{i}^{l} & h_{i}^{R}\end{bmatrix}};} & (60)\end{matrix}$where h_(i) ^(R)=Re{h_(i)},h_(i) ^(l)=Im{h_(i)}.

Similarly to previous derivations above we denote

_(i)=y _(i)− _(i) ^(h),+E,u $\begin{matrix}{\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {{\min\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2}\left( {\sum\limits_{i}{\left( {\overset{\Cap}{\underset{\_}{e}}}_{i,l} \right)^{T}{\Lambda^{- 1}\left( {\overset{\Cap}{\underset{\_}{e}}}_{i,l} \right)}}} \right)} \right)} - {\frac{1}{2}{\sum\limits_{i}{\left( {\underset{\_}{e}}_{i}^{eq} \right)^{T}{\Lambda^{- 1}\left( {\underset{\_}{e}}_{i}^{eq} \right)}}}}}} \right. = {\min\limits_{l \in D_{j\quad 1}}\left( {\frac{1}{2}\left( {{\sum\limits_{i}{\left( {\overset{\Cap}{\underset{\_}{e}}}_{i,l} \right)^{T}{\Lambda^{- 1}\left( {\overset{\Cap}{\underset{\_}{e}}}_{i,l} \right)}}} - {\left( {\underset{\_}{e}}_{i}^{eq} \right)^{T}{\Lambda^{- 1}\left( {\underset{\_}{e}}_{i}^{eq} \right)}}} \right)} \right)}} & (61) \\{\quad{{{\underset{\_}{e}}_{i}^{eq} - {H_{\Delta} \cdot \left( {{\overset{\Cap}{\underset{\_}{S}}}_{i - \Delta} - {\underset{\_}{S}}_{i - \Delta}} \right)}} = {{{\underset{\_}{e}}_{i}^{eq} - {H_{\Delta} \cdot \underset{\_}{\Delta\quad S}}} = \underset{\_}{\overset{\Cap}{e}}}}} & (62) \\{\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2} \cdot}} \right.{\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L - 1}{\left( {{\underset{\_}{e}}_{i}^{eq} - {H_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)^{T}{\Lambda^{- 1}\left( {{\underset{\_}{e}}_{i}^{eq} - {H_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)}}} - {\left( {\underset{\_}{e}}_{i}^{eq} \right)^{T}{\Lambda^{- 1}\left( {\underset{\_}{e}}_{i}^{eq} \right)}}} \right)}} & (63)\end{matrix}$Note that the above relation does not consider the rotation detailed inthe section above entitled “Rotation and Relation to InterferenceCancellation”. Considering the rotation, Λ⁻¹ is selected out of thearray of eight Λ⁻¹ matrices (Equation 20), rather than using a constantΛ⁻¹.

Taking into account rotation modifies the expression presented above tothe following relationship where Λ_(k) ⁻¹ changes across time:$\begin{matrix}\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L - 1}{\left( {{\underset{\_}{e}}_{i}^{eq} - {H_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)^{T}{\Lambda_{k + i}^{- 1}\left( {{\underset{\_}{e}}_{i}^{eq} - {H_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)}}} - {\left( e_{i}^{eq} \right)^{T}{\Lambda_{k + i}^{- 1}\left( {\underset{\_}{e}}_{i}^{eq} \right)}}} \right)}}} \right. & (64)\end{matrix}$Note that the expression presented above presents the Max-Log solutionrather than a solution of the type described in U.S. Pat. No. 6,529,559cited supra. Since the correlation matrix stretches the symbol plane ateach burst into an unknown direction, the max-log is needed. Using anI/Q whitened version of the path errors, however, may solve thisproblem.

Model Extension 2: PSP

As detailed supra, the noise may be formulated as a first orderautoregressive (AR) process. The process correlation coefficient α canbe estimated from the training sequence:n _(k) ={circumflex over (α)}·n _(k−1) +w _(k) ŵ _(k) =n _(k)−{circumflex over (α)}·n _(k−1)  (65)where ŵ_(k) is a “temporally white” noise. Note that here the noise iscomplex and is not represented by vector notation as in the previoussection. In addition, we relax the rotation assumption for simplicity.In similarity to the derivation steps outlined above:

_(i) =e _(i) ^(eq) −h _(Δ)·(

_(i−Δ) −S _(i−Δ))=e _(i) ^(eq) −h _(Δ) +The above expression can also be extended for the case where e_(i) has atemporal correlation as follows:η_(i) =e _(i) −·e _(i−1)  (67)In the above equation, η_(i) represents a temporally white additiveGaussian noise. In this case, it is assumed that the error signal e_(i)obeys a first order AR model with the coefficient α. Therefore:$\begin{matrix}{{\left. \begin{matrix}{{\overset{\Cap}{\eta}}_{i} = {{y_{i}{\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot {\overset{\Cap}{S}}_{i - n}}}} - {\alpha \cdot {\overset{\Cap}{e}}_{i - 1}}}} \\{= {y_{i} - {\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot S_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}} + {h_{\Delta} \cdot S_{i - \Delta}} - {\alpha \cdot {\overset{\Cap}{e}}_{i - 1}}}} \\{= {y_{i} - {\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot S_{i - n}}} - {h_{\Delta} \cdot {\overset{\Cap}{S}}_{i - \Delta}} + {h_{\Delta} \cdot S_{i - \Delta}} - {\alpha \cdot \left\lbrack {e_{i - 1}^{eq} - {{h_{\Delta - 1} \cdot \Delta}\quad S}} \right\rbrack}}} \\{= {y_{i} - {\sum\limits_{n = 0}^{L - 1}{h_{n} \cdot S_{i - n}}} - {\alpha \cdot e_{i - 1}^{eq}} - {{h_{\Delta} \cdot \Delta}\quad S} - {{\alpha \cdot h_{\Delta - 1} \cdot \Delta}\quad S}}} \\{= {\eta_{i}^{eq} - {{\left\lbrack {h_{\Delta} - {\alpha \cdot h_{\Delta - 1}}} \right\rbrack \cdot \Delta}\quad S}}}\end{matrix}\Rightarrow{\overset{\Cap}{\eta}}_{i} \right. = {\eta_{i}^{eq} - {{{\overset{\sim}{h}}_{\Delta} \cdot \Delta}\quad S}}};{{{where}\quad{\overset{\sim}{h}}_{\Delta}} = \left\lbrack {h_{\Delta} - {\alpha \cdot h_{\Delta - 1}}} \right\rbrack}} & (68)\end{matrix}$

Since

_(i) and η_(i) ^(eq) obey the same relationship as

_(i) and e_(i) ^(eq), the remainder of the derivat similar with theexception of a modified channel. The modified channel is the originalchannel filtered by the filter [1,−α]. $\begin{matrix}{\left. \Rightarrow\quad{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2\quad\sigma^{2}} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L}{{\eta_{i}^{eq} - {{\left\lbrack {h_{i} - {\alpha \cdot h_{i - 1}}} \right\rbrack \cdot \Delta}\quad S_{l}}}}^{2}} - {\eta_{i}^{eq}}^{2}} \right)}}} \right. = {\frac{1}{2\quad\sigma^{2}} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L}{{\eta_{i}^{eq} - {{{\overset{\sim}{h}}_{i} \cdot \Delta}\quad S_{l}}}}^{2}} - {\eta_{i}^{eq}}^{2}} \right)}}} & (69)\end{matrix}$Since I/Q correlation is not taken into account here, the solutionoutlined in U.S. Pat. No. 6,529,559 cited supra, can be used here aswell.

Model Extension 3: Vector PSP

In this section both the PSP solution and the vector representation aretaken into account. As detailed hereinabove, the predicting matrix C, isnot necessarily a matrix representing a complex number.n _(k) =Ĉ·n _(k−1) +w _(k) ŵ _(k) =n _(k) −Ĉ·n _(k−1).  (70)An I/Q de-correlation matrix is used in this model as well, as detailedsupra. The derivation used above can be extended to vector form in thefollowing manner: $\begin{matrix}\begin{matrix}{\quad{{\underset{\_}{\overset{\Cap}{\eta}}}_{i} = {{\underset{\_}{y}}_{i} - {\sum\limits_{n = 0}^{L - 1}{H_{n} \cdot {\underset{\_}{\overset{\Cap}{S}}}_{i - n}}} - {C \cdot {\underset{\_}{\overset{\Cap}{e}}}_{i - 1}}}}} \\{= {{\underset{\_}{y}}_{i} - {\sum\limits_{n = 0}^{L - 1}{H_{n} \cdot {\underset{\_}{S}}_{i - n}}} - {H_{\Delta} \cdot {\underset{\_}{\overset{\Cap}{S}}}_{i - \Delta}} + {H_{\Delta} \cdot {\underset{\_}{S}}_{i - \Delta}} - {C \cdot {\underset{\_}{\overset{\Cap}{e}}}_{i - 1}}}} \\{= {{\underset{\_}{y}}_{i} - {\sum\limits_{n = 0}^{L - 1}{H_{n} \cdot {\underset{\_}{S}}_{i - n}}} - {H_{\Delta} \cdot {\underset{\_}{\overset{\Cap}{S}}}_{i - \Delta}} + {H_{\Delta} \cdot {\underset{\_}{S}}_{i - \Delta}} -}} \\{C \cdot \left\lbrack {{\underset{\_}{e}}_{i - 1}^{eq} - {H_{\Delta - 1} \cdot \underset{\_}{\Delta\quad S}}} \right\rbrack} \\{= {{\underset{\_}{y}}_{i} - {\sum\limits_{n = 0}^{L - 1}{H_{n} \cdot {\underset{\_}{S}}_{i - n}}} - {C \cdot {\underset{\_}{e}}_{i - 1}^{eq}} - {H_{\Delta} \cdot \underset{\_}{\Delta\quad S}} - {C \cdot H_{\Delta - 1} \cdot \underset{\_}{\Delta\quad S}}}} \\{= {{\underset{\_}{\eta}}_{i}^{eq} - {\left\lbrack {H_{\Delta} - {C \cdot H_{\Delta - 1}}} \right\rbrack \cdot \underset{\_}{\Delta\quad S}}}} \\{{\left. \Rightarrow{\underset{\_}{\overset{\Cap}{\eta}}}_{i} \right. = {{\underset{\_}{\eta}}_{i}^{eq} - {{\overset{\sim}{H}}_{\Delta} \cdot \underset{\_}{\Delta\quad S}}}};{{{where}\quad{\overset{\sim}{H}}_{\Delta}} = \left\lbrack {H_{\Delta} - {C \cdot H_{\Delta - 1}}} \right\rbrack}}\end{matrix} & (71)\end{matrix}$Note that the channel coefficients H_(i) are defined as above. Since_(i) and η _(i) ^(eq) obey the same relationship as

_(i) and e _(i) ^(eq) the remainder of the derivation is as describedabove, 0 only w channel: {tilde over (H)}_(i)=H_(i)−C·H_(i−1)$\begin{matrix}{\quad\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L}{\left( {{\underset{\_}{\eta}}_{i}^{eq} - {{\overset{\sim}{H}}_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)^{T}{\Lambda^{- 1}\left( {{\underset{\_}{\eta}}_{i}^{eq} - {{\overset{\sim}{H}}_{i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)}}} - {\left( {\underset{\_}{\eta}}_{i}^{eq} \right)^{T}{\Lambda^{- 1}\left( {\underset{\_}{\eta}}_{i}^{eq} \right)}}} \right)}}} \right.} & (72)\end{matrix}$The Λ in the above formula is the correlation matrix of the “temporallywhite” noise η _(i). Note that rotation is not taken into account in theabove formula.

When taking into account the rotation, two elements in the above formulamust be considered: Λ,C. Since both Λ and C are rotated in a symbol bysymbol fashion, the rotation must be incorporated into the equation asfollows: $\begin{matrix}{\quad{\left. \Rightarrow{{{LLR}\left( {b_{j} = 1} \right)} \approx {\frac{1}{2} \cdot {\min\limits_{l \in D_{j\quad 1}}\left( {{\sum\limits_{i = 0}^{L}{\left( {{\underset{\_}{\eta}}_{i}^{eq} - {{\overset{\sim}{H}}_{k,i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)^{T}{\Lambda_{k + i}^{- 1}\left( {{\underset{\_}{\eta}}_{i}^{eq} - {{\overset{\sim}{H}}_{k,i} \cdot {\underset{\_}{\Delta\quad S}}_{l}}} \right)}}} - {\left( {\underset{\_}{\eta}}_{i}^{eq} \right)^{T}{\Lambda_{k + i}^{- 1}\left( {\underset{\_}{\eta}}_{i}^{eq} \right)}}} \right)}}} \right.{{\overset{\sim}{H}}_{k,i} = {H_{i} - {C_{k + i} \cdot H_{i - 1}}}}}} & (73)\end{matrix}$

The above equation indicates that both Λ and C are rotated according to:(1) k which denotes the error symbol index, and (2) i which denotes thechannel taps. When creating the equivalent channel {tilde over (H)}, therotation of C should be included as in the following example. Assumethat the SVG input comprises the right side of the burst. As describedsupra, only eight C matrices are utilized. Table 1 below describes thenew equivalent channel taps for different values of k. In this exampleL=3 and the original channel taps are given by {H⁻¹=0,H₀,H₁,H₂,H₃=0}.TABLE 1 Calculation of channel taps for the right side of the burst inrotated vector PSP ((k))₈ → Initial C Ĥ₀ Ĥ₁ Ĥ₂ Ĥ₃ 0 → C₀ H₀ − C₀ · H⁻¹ =H₀ H₁ − C₁ · H₀ H₂ − C₂ · H₁ H₃ − C₃ · H₂ = −C₃ · H₂ 1 → C₁ H₀ − C₁ ·H⁻¹ = H₀ H₁ − C₂ · H₀ H₂ − C₃ · H₁ H₃ − C₄ · H₂ = −C₄ · H₂ . . . . . . .. . . . . . . . 4 → C₄ H₀ − C₄ · H⁻¹ = H₀ H₁ − C₅ · H₀ H₂ − C₆ · H₁ H₃ −C₇ · H₂ = −C₇ · H₂ . . . . . . . . . . . . . . . 7 → C₇ H₀ − C₇ · H⁻¹ =H₀ H₁ − C₀ · H₀ H₂ − C₁ · H₁ H₃ − C₂ · H₂ = −C₂ · H₂Note that in Table 1 above, the notation ((a))_(b) denotes mod(a,b).

In the event the SVG input comprises the left side of the burst, thefollowing Table 2 below presents the new equivalent channel: TABLE 2Calculation of channel taps for the left side of the burst in rotatedvector PSP ((k))₈ → Initial C Ĥ₀ Ĥ₁ Ĥ₂ Ĥ₃ 0 → C₀ H₀ − C₀ · H⁻¹ = H₀ H₁ −C₇ · H₀ H₂ − C₆ · H₁ H₃ − C₅ · H₂ = −C₅ · H₂ 1 → C₁ H₀ − C₁ · H⁻¹ = H₀H₁ − C₀ · H₀ H₂ − C₇ · H₁ H₃ − C₆ · H₂ = −C₆ · H₂ . . . . . . . . . . .. . . .

Simulation Results

Simulation results are now presented for the PSK/SAIC algorithms of thepresent invention described above. A graph illustrating the BLER curvefor a receiver implementing the SAIC scheme of the present invention isshown in FIG. 11. The EGPRS system is a Time Division Multiple Access(TDMA) system wherein eight users are able to share the same carrierfrequency. In an EGPRS transmitter, the data bits are encoded with arate ⅓ convolutional encoder, interleaved and mapped to 8-ary symbols.The resultant coded data symbols together with the training sequence areassembled into a burst of 142 symbols as shown in FIG. 2.

The burst is then modulated using 3π/8-offset 8PSK with Gaussian pulseshaping in accordance with the GSM standard. The modulated output istransmitted over an additive white Gaussian noise channel as describedabove. An MLSE type equalizer with a Least Squares type channelestimator was used in the receiver.

The simulations were performed using a software-based modem assuming thestatic MCS5 coding scheme. The results of the simulation were comparedusing block error rate (BLER) as the criteria. The solid line 1100represents the results of a reference receiver with C implemented. Thedashed line 1102 represents the SAIC simulation environment referencereceiver with squared metric equalizer followed by a suitable SVGmodule. It is important to note that unlike the reference receiver thisSAIC simulation environment receiver does not incorporate PSPcorrection.

The dotted curve 1106 represents the PSP de-correlation algorithmresults wherein both the equalizer and the SVG module includes whiteningof both the I/Q correlation and the temporal correlation in its model.The dash-dotted curve 1104 represents a hybrid solution where a regularsquared metric equalizer is applied followed by a SVG module based onthe PSP de-correlation receiver. In this case the model characterizingmatrices (i.e. C, Λ) are estimated post equalization.

Several conclusions may be drawn from the results presented. First, thePSP de-correlation algorithm outperforms the other algorithms where asingle interference signal (i.e. DTS1) is applied. For a static channelDTS1 the PSP de-correlation gain approaches 2.5 dB relative to thereference receiver.

GSM EDGE Embodiment

A GSM EGPRS mobile station constructed to comprise means for performingthe channel tracking method of the present invention is presented. Ablock diagram illustrating the processing blocks of a GSM EGPRS mobilestation in more detail including RF, baseband and signal processingblocks is shown in FIG. 12. The radio station is designed to providereliable data communications at rates of up to 470 kbit/s. The GSM EGPRSmobile station, generally referenced 1200, comprises a transmitter andreceiver divided into the following sections: signal processingcircuitry 1218, baseband codec 1212 and RF circuitry section 1206.

In the transmit direction, the signal processing portion functions toprotect the data so as to provide reliable communications from thetransmitter to the base station 1202 over the channel 1204. Severalprocesses performed by the channel coding block 1222 are used to protectthe user data 1228 including cyclic redundancy code (CRC) check,convolutional coding, interleaving and burst assembly. The resultantdata is assembled into bursts whereby guard and trail symbols are addedin addition to a training sequence midamble that is added to the middleof the burst. Note that both the user data and the signaling informationgo through similar processing. The assembled burst is then modulated bya modulator 1220 which may be implemented as a 3π/8 offset 8PSKmodulator.

In the receive direction, the output of the baseband codec isdemodulated using a complementary 8PSK demodulator 1224. Severalprocesses performed by the channel decoding block 1226 in the signalprocessing section are then applied to the demodulated output. Theprocesses performed include burst disassembly, channel estimation,equalization utilizing the modified metric as taught by the presentinvention, described in detail supra, de-interleaving, convolutionaldecoding and CRC check. Optionally, soft value generation utilizing themodified metric as taught by the present invention and soft symbol tosoft bit conversion may also be performed depending on the particularimplementation.

The baseband codec converts the transmit and receive data into analogand digital signals, respectively, via D/A converter 1214 and A/Dconverter 1216. The transmit D/A converter provides analog baseband Iand Q signals to the transmitter 1208 in the RF circuitry section. The Iand Q signals are used to modulate the carrier for transmission over thechannel.

In the receive direction, the signal transmitted by the base stationover the channel is received by the receiver circuitry 1210. The analogsignals I and Q output from the receiver are converted back into adigital data stream via the A/D converter. This I and Q digital datastream is filtered and demodulated by the 8PSK demodulator before beinginput to the channel decoding block 1226. Several processes performed bysignal processing block are then applied to the demodulated output.

In addition, the mobile station performs other functions that may beconsidered higher level such as synchronization, frequency and timeacquisition and tracking, monitoring, measurements of received signalstrength and control of the radio. Other functions include handling theuser interface, signaling between the mobile station and the network,the SIM interface, etc.

Computer Embodiment

In alternative embodiments, the present invention may be applicable toimplementations of the invention in integrated circuits or chip sets,wired or wireless implementations, switching system products andtransmission system products. For example, a computer is operative toexecute software adapted to implement the SAIC scheme of the presentinvention. A block diagram illustrating an example computer processingsystem adapted to perform the SAIC scheme of the present invention isshown in FIG. 13. The system may be incorporated within a communicationsdevice such as a receiver or transceiver, some or all of which may beimplemented in software, hardware or a combination of software andhardware.

The computer system, generally referenced 1300, comprises a processor1302 which may include a digital signal processor (DSP), centralprocessing unit (CPU), microcontroller, microprocessor, microcomputer,ASIC or FPGA core. The system also comprises static read only memory1304 and dynamic main memory 1310 all in communication with theprocessor. The processor is also in communication, via bus 1306, with anumber of peripheral devices that are also included in the computersystem.

In the receive direction, signals received over the channel 1316 arefirst input to the RF front end circuitry 1314 which comprises areceiver section (not shown) and a transmitter section (not shown).Baseband samples of the received signal are generated by the A/Dconverter 1318 and read by the processor. Baseband samples generated bythe processor are converted to analog by D/A converter 1312 before beinginput to the transmitter for transmission over the channel via the RFfront end.

One or more communication lines 1322 are connected to the system via I/Ointerface 1320. A user interface 1324 responds to user inputs andprovides feedback and other status information. A host interface 1326connects a host device 1328 to the system. The host is adapted toconfigure, control and maintain the operation of the system. The systemalso comprises magnetic storage device 1308 for storing applicationprograms and data. The system comprises computer readable storage mediumthat may include any suitable memory means, including but not limitedto, magnetic storage, optical storage, semiconductor volatile ornon-volatile memory, biological memory devices, or any other memorystorage device.

The SAIC software is adapted to reside on a computer readable medium,such as a magnetic disk within a disk drive unit. Alternatively, thecomputer readable medium may comprise a floppy disk, removable harddisk, Flash memory card, EEROM based memory, bubble memory storage, ROMstorage, distribution media, intermediate storage media, executionmemory of a computer, and any other medium or device capable of storingfor later reading by a computer a computer program implementing themethod of this invention. The software adapted to implement the SAICscheme of the present invention may also reside, in whole or in part, inthe static or dynamic main memories or in firmware within the processorof the computer system (i.e. within microcontroller, microprocessor ormicrocomputer internal memory).

In alternative embodiments, the SAIC scheme of the present invention maybe applicable to implementations of the invention in integratedcircuits, field programmable gate arrays (FPGAs), chip sets orapplication specific integrated circuits (ASICs), wired or wirelessimplementations and other communication system products.

Other digital computer system configurations can also be employed toperform the SAIC method of the present invention, and to the extent thata particular system configuration is capable of performing the method ofthis invention, it is equivalent to the representative digital computersystem of FIG. 13 and within the spirit and scope of this invention.

Once they are programmed to perform particular functions pursuant toinstructions from program software that implements the method of thisinvention, such digital computer systems in effect become specialpurpose computers particular to the method of this invention. Thetechniques necessary for this are well-known to those skilled in the artof computer systems.

It is noted that computer programs implementing the method of thisinvention will commonly be distributed to users on a distribution mediumsuch as floppy disk or CD-ROM or may be downloaded over a network suchas the Internet using FTP, HTTP, or other suitable protocols. Fromthere, they will often be copied to a hard disk or a similarintermediate storage medium. When the programs are to be run, they willbe loaded either from their distribution medium or their intermediatestorage medium into the execution memory of the computer, configuringthe computer to act in accordance with the method of this invention. Allthese operations are well-known to those skilled in the art of computersystems.

It is intended that the appended claims cover all such features andadvantages of the invention that fall within the spirit and scope of thepresent invention. As numerous modifications and changes will readilyoccur to those skilled in the art, it is intended that the invention notbe limited to the limited number of embodiments described herein.Accordingly, it will be appreciated that all suitable variations,modifications and equivalents may be resorted to, falling within thespirit and scope of the present invention.

1. A method of computing a metric to be used in determining an estimateof a most likely sequence of symbols transmitted over a channel from aplurality of received samples, each received sample comprising aninformation component and an interference component, said methodcomprising the steps of: estimating an error vector by subtracting theconvolution of known training sequence symbols with an estimate of saidchannel from said plurality of received samples corresponding to saidtraining sequence; estimating a noise correlation matrix by processingreal and imaginary components of said error vector; computing aplurality of summations by processing said plurality of receivedsamples, said noise correlation matrix and a plurality of hypotheses ofsymbols that have been passed through said channel; and determining aminimum summation from said plurality of summations resulting in saidmetric.
 2. The method according to claim 1, further comprising the stepof calculating a temporal error correlation by correlating betweenconsecutive samples of said error vector and incorporating the resultantcorrelation into said computation of a plurality of summations by meansof error prediction.
 3. A method of computing a metric to be used indetermining, from a plurality of received samples, an estimate of a mostlikely sequence of symbols transmitted over a channel, each receivedsample comprising an information component and an interferencecomponent, said method comprising the steps of: estimating an errorvector by subtracting the convolution of known training sequence symbolswith an estimate of said channel from said plurality of received samplescorresponding to said training sequence; de-rotating said error vectorto generate a de-rotated error vector; estimating a noise correlationmatrix by processing real and imaginary components of said de-rotatederror vector; computing a rotation compensated noise correlation matrixby processing said noise correlation matrix in accordance with acorresponding sample index; computing a plurality of summations byprocessing said plurality of received samples, said rotation compensatednoise correlation matrix and a plurality of hypotheses of symbols thathave been passed through said channel; and determining a minimumsummation from said plurality of summations resulting in said metric. 4.The method according to claim 3, wherein said information componentcomprises an 8PSK modulated signal.
 5. The method according to claim 3,wherein said interference component comprises a GMSK modulated signal.6. The method according to claim 3, wherein said rotation compensatednoise correlation matrix is chosen from a group of eight possiblematrices, each matrix corresponding to a different rotation offsetbetween GMSK and 8PSK wherein 8PSK has 3π/8 offset rotation and GMSK isconsidered BPSK with π/2, resulting in an offset rotation difference ofπ/8.
 7. The method according to claim 3, further comprising the step ofcalculating a temporal error correlation by correlating betweenconsecutive samples of said error vector and incorporating the resultantcorrelation into said computation of a plurality of summations by meansof error prediction.
 8. The method according to claim 3, wherein saiderror vector is de-rotated by an amount π/8 to generate said de-rotatederror vector.
 9. A computer-readable medium storing a computer programimplementing the method of claim
 3. 10. A digital computer systemprogrammed to perform the method of claim
 3. 11. A method ofimplementing an equalizer in a radio receiver subjected to co-channelinterference, said method comprising the steps of: receiving a pluralityof received samples, each received sample comprising an informationcomponent and an interference component; calculating and assigning ametric to each sequence of symbols to be considered; wherein the step ofcalculating said metric comprises the steps of: estimating an errorvector by subtracting the convolution of known training sequence symbolswith an estimate of said channel from said plurality of received samplescorresponding to said training sequence; de-rotating said error vectorto generate a de-rotated error vector; estimating a noise correlationmatrix by processing real and imaginary components of said de-rotatederror vector; computing a rotation compensated noise correlation matrixby processing said noise correlation matrix in accordance with acorresponding sample index; computing a plurality of summations byprocessing said plurality of received samples, said rotation compensatednoise correlation matrix and a plurality of hypotheses of symbols thathave been passed through said channel; determining a minimum summationfrom said plurality of summations resulting in a lowest metricrepresenting a most likely sequence of symbols transmitted over saidchannel; and removing intersymbol interference introduced by saidchannel including said co-channel interference utilizing said lowestmetric.
 12. The method according to claim 11, wherein said informationcomponent comprises an 8PSK block code modulated signal.
 13. The methodaccording to claim 11, wherein said interference component comprises aGMSK modulated signal.
 14. The method according to claim 11, whereinsaid rotation compensated noise correlation matrix is chosen from agroup of eight possible matrices, each matrix corresponding to one ofeight possible sample indexes of an 8PSK modulated signal.
 15. Themethod according to claim 11, wherein said error vector is de-rotated byamount π/8 to generate said de-rotated error vector.
 16. Acomputer-readable medium storing a computer program implementing themethod of claim
 11. 17. A digital computer system programmed to performthe method of claim
 11. 18. A computer program product characterized bythat upon loading it into computer memory a metric calculation processis executed, said computer program product comprising: a computeruseable medium having computer readable program code means embodied insaid medium for computing a metric to be used in determining an estimateof a most likely sequence of symbols transmitted over a channel from aplurality of received samples, each received sample comprising aninformation component and an interference component, said computerprogram product comprising: computer readable program code means forestimating an error vector by subtracting the convolution of knowntraining sequence symbols with an estimate of said channel from saidplurality of received samples corresponding to said training sequence;computer readable program code means for estimating a noise correlationmatrix by processing real and imaginary components of said rotated errorvector; computer readable program code means for computing a pluralityof summations by processing said plurality of received samples, saidnoise correlation matrix and a plurality of hypotheses of symbols thathave been passed through said channel; and computer readable programcode means for determining a minimum summation from said plurality ofsummations resulting in said metric.
 19. The computer program productaccording to claim 18, further comprising: computer readable programcode means for de-rotating said error vector to generate a de-rotatederror vector; computer readable program code means for estimating saidnoise correlation matrix by processing real and imaginary components ofsaid de-rotated error vector; and computer readable program code meansfor computing a rotation compensated noise correlation matrix byprocessing said noise correlation matrix in accordance with acorresponding sample index.
 20. The computer program product accordingto claim 18, further comprising computer readable program code means forcalculating a temporal error correlation by correlating betweenconsecutive samples of said error vector and incorporating said temporalerror correlation into said computation of a plurality of summations bymeans of error prediction.
 21. A radio receiver coupled to a singleantenna, comprising: a radio frequency (RF) receiver front end circuitfor receiving a radio signal transmitted over a channel anddownconverting the received radio signal to a baseband signal, saidreceived radio signal comprising an information component and aninterference component; a demodulator adapted to demodulate saidbaseband signal in accordance with the modulation scheme used togenerate said transmitted radio signal; a channel estimation moduleadapted to calculate a channel estimate by processing a receivedtraining sequence and a known training sequence; an equalizer adapted toremove intersymbol interference introduced by said channel utilizing ametric calculation stage and an estimate of said channel, said metriccalculation stage comprising processing means adapted to; estimate anerror vector by subtracting the convolution of known training sequencesymbols with said estimate of said channel from said plurality ofreceived samples corresponding to said training sequence; estimate anoise correlation matrix by processing real and imaginary components ofsaid =error vector; compute a plurality of summations by processing saidplurality of received samples, said noise correlation matrix and aplurality of hypotheses of symbols that have been passed through saidchannel; determine a minimum summation from said plurality of summationsresulting in said metric; and a decoder adapted to decode the output ofsaid equalizer to generate output data therefrom.
 22. The methodaccording to claim 21, wherein said equalizer processing means isfurther adapted to: de-rotate said error vector to generate a de-rotatederror vector; estimate said noise correlation matrix by processing realand imaginary components of said de-rotated error vector; and compute arotation compensated noise correlation matrix by processing said noisecorrelation matrix in accordance with a corresponding sample index. 23.The method according to claim 21, wherein said equalizer processingmeans is further adapted to calculate a temporal error correlation bycorrelating between consecutive samples of said error vector andincorporating said temporal error correlation into said computation of aplurality of summations by means of error prediction.
 24. The receiveraccording to claim 21, wherein said receiver is adapted to receive anddecode a global system for mobile communications (GSM) cellular signal.25. A method of generating soft values from hard symbol decisions outputof an equalizer, said method comprising the steps of: calculating anerror matrix incorporating consideration for I/Q correlation of noise inan interferer signal; estimating an error vector by subtracting theconvolution of known training sequence symbols with an estimate of saidchannel from a plurality of received samples corresponding to saidtraining sequence; estimating a noise correlation matrix by processingreal and imaginary components of said error vector; computing aplurality of summations by processing said plurality of receivedsamples, said noise correlation matrix and a plurality of hypotheses ofsymbols that have been passed through said channel; determining aminimum summation from said plurality of summations resulting in anerror metric; determining a conditional probability of said plurality ofreceived samples given said hard symbol decision sequence; andcalculating log likelihood ratio (LLR) of said conditional probabilityto yield said soft decision values.
 26. The method according to claim25, further comprising the steps of: de-rotating said error vector togenerate a de-rotated error vector; estimating said noise correlationmatrix by processing real and imaginary components of said de-rotatederror vector; and computing a rotation compensated noise correlationmatrix by processing said noise correlation matrix in accordance with acorresponding sample index.
 27. The method according to claim 25,further comprising the steps of calculating a temporal error correlationby correlating between consecutive samples of said error vector andincorporating said temporal error correlation into said computation of aplurality of summations by means of error prediction.